h sub spl infin control of discrete time uncertain systems this paper considers h sub spl infin control problems involving discrete time uncertain linear systems the uncertainty is supposed to belong to convex bounded domains and no additional assumptions are made as for instance matching conditions two h sub spl infin guaranteed cost control problems are solved the first one concerns the determination of a state feedback gain if one exists in such way the h sub spl infin norm of a certain transfer function remains bounded by a prespecified h sub spl infin level for all possible models the second one includes this bound as an additional variable to be minimized to achieve the smallest feasible limiting bound the results follow from the simple geometry of those problems which are shown to be convex in the particular parametric space under consideration an example illustrates the theory

endomorphism rings of permutation modules let k be an algebraically closed field of characteristic p and g a finite group then the permutation module kpg of g on the cosets of a sylow p subgroup p is via fitting correspondence strongly related to its endomorphism ring endkg kpg on the other hand each green correspondent in g of a weight module of g occurs as a direct summand of kpg this fact suggests to analyze both structures the permutation module and the associated endomorphism ring towards hints at a proof for alperin s weight conjecture we present a selection of such investigations for different groups and characteristics in particular we focus on the socle and head constituents of the indecomposable direct summands of kpg and of the pims of ee

output feedback direct adaptive fuzzy controller based on frequency domain methods this paper describes a design method that guarantees the stability of an adaptive fuzzy control system the system consists of an unstable plant with an irrational transfer function a takagi sugeno fuzzy adaptive controller a nonlinear reference model and an adaptation mechanism the gradient based adaptation mechanism changes the consequents of the controller rules in such a way that the closed loop system behaves like the reference model the proposed design procedure utilizes frequency domain methods in the forms of the nyquist and circle criteria it is assumed that the function of the fuzzy controller is a nonlinearity described by a sector condition this condition means that the controller function lies between two lines passing through the origin in this method the function of the fuzzy controller is verified during online adaptation therefore it stays in the allowed sector this method is illustrated by an example of a control system containing an unstable plant with a transport delay the main contribution of this paper is to use frequency methods combined with adaptive fuzzy control these methods have previously been used for nonadaptive fuzzy control but in this paper they are used for the first time for adaptive fuzzy control

adaptive control of non linear continuous time systems using neural networks general relative degree and mimo cases multilayer neural networks are used in a non linear adaptive control problem the plant is an unknown feedback linearizable continuous time system with relative degree 1 the single input single output system is studied first and then the methodology is extended to control square multi input multi output systems the control objective is for the plant to track a reference trajectory and the control law is defined in terms of the outputs of the neural networks the parameters of the networks are updated on line according to an augmented tracking error and the network derivatives a local convergence theorem is given on the convergence of the tracking error this control algorithm is applied to control a two input two output relative degree two system

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

fuzzy control turns 50 in 2015 we celebrate the 50th anniversary of fuzzy sets ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in fss see 1 ten years is at the same time a long period and short time thinking to the inner dynamics of research this paper presented for these 50 years of fuzzy sets is taking into account both thoughts a first part presents a quick recap of the history of fuzzy control from model free design based on human reasoning to quasi lpv linear parameter varying model based control design via some milestones and key applications the second part shows where we arrived and what the improvements are since the milestone of the first 40 years a last part is devoted to discussion and possible future research topics

fuzzy learning control for a flexible link robot there are two main drawbacks in fuzzy control 1 the design of fuzzy controllers is usually performed in an ad hoc manner where it is often difficult to choose some of the controller parameters and 2 the fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur in this paper we illustrate these two problems on a two link flexible robot testbed by 1 developing implementing and evaluating a fuzzy controller for the robotic mechanism and 2 illustrating that payload variations can have negative effects on the performance of a well designed fuzzy control system next we show how to develop and implement a fuzzy model reference learning controller for the flexible robot and illustrate that it can automatically synthesize a rule base for a fuzzy controller that will achieve comparable performance to the case where it was manually constructed and automatically tune the fuzzy controller so that it can adapt to variations in the payload

a less conservative lmi condition for the robust stability of discrete time uncertain systems abstract in this paper a less conservative condition for the robust stability of uncertain discrete time linear systems is proposed the uncertain parameters assumed to be time invariant are supposed to belong to convex bounded domains polytope type uncertainty the stability condition is formulated in terms of a set of linear matrix inequalities involving only the vertices of the polytope domain a simple and numerically efficient feasibility test provides a set of lyapunov matrices whose convex combination can be used to assess the stability of any dynamic matrix inside the uncertainty domain examples illustrate the results

robustifying nonlinear systems using high order neural network controllers a robust control methodology for affine control of nonlinear dynamical systems is developed in this paper a correction control signal is added to a nominal controller designed to guarantee a desired performance for the corresponding nominal system to render the actual system uniformly and ultimately bounded the control signal is smooth and does not require a priori knowledge of an upper bound on the modeling error and or optimal weight values simulations performed on a simple nonlinear system illustrate the approach

a linear programming oriented procedure for quadratic stabilization of uncertain systems abstract this paper gives a new necessary and sufficient condition for linear quadratic stabilization of linear uncertain systems when both the dynamic as well as the control matrix are subject to uncertainty a constructive numerical procedure is defined to check the condition and it furthermore provides a stabilizing linear feedback gain some experiments are presented

adaptive control of mimo time varying systems with indicator function based parametrization abstract this paper studies a new solution framework for adaptive control of a class of mimo time varying systems with indicator function based parametrization motivated by a general discrete time mimo takagi sugeno t s fuzzy system model in an input output form with unknown parameters an indicator membership function based parametrization has some favorable capacity to deal with certain large parameter variations a new discrete time mimo system prediction model is derived for approximating a nonlinear dynamic system and its system properties are clarified an adaptive control scheme is developed with desired controller parametrization and stable parameter estimation for control of such uncertain mimo time varying systems a control singularity problem is addressed and the closed loop stability and output tracking properties are analyzed this work provides a new method for multivariable t s fuzzy system modeling and adaptive control an illustrative example and simulation results are presented to demonstrate the proposed novel concepts and to verify the desired adaptive control system performance

a survey of adaptive fuzzy controllers nonlinearities and classifications adaptive fuzzy controllers afcs i e fuzzy controllers using heuristic expert knowledge and equipped with adaption ability are widely used in the industry in the present days as they are capable of dealing with ill formulated nonlinear systems where exact mathematical formulas are not known or partially described nonlinear systems afcs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities over the last two decades many different approaches toward adaptive fuzzy control have been reported in this paper we recapitulate the latest research works related to afcs and provide an up to date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled we categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems nonlinear systems with external disturbances nonlinear systems with some special type of nonlinearities nonaffine nonlinear systems and strict feedback nonlinear systems it turns out that many existing methods are subject to various limitations and none of them is capable of controlling a general nonlinear systems hence it is still an open problem to design and develop a universal afc for a general class of nonlinear systems

fuzzy adaptive control of a certain class of siso discrete time processes in this manuscript we address the problem of the stability of a certain class of siso discrete time processes controlled by an adaptive fuzzy controller by using lyapunov stability theory these results were recently obtained for adaptive neural controllers and are extended here to adaptive fuzzy controllers of sugeno s type in order to achieve tracking of a reference signal with this kind of fuzzy system we allow both the membership functions and the consequent part of the rules to be adjusted by a parameter adaptation law we first present the gradient based steepest descent adaptation law and we argue that this gradient based adaptation law can be simplified dramatically thereafter we show the asymptotic stability of the overall system the convergence of the tracking error to zero when using this simplified parameters adjustment law unfortunately this result can only be proved when the outputs of the fuzzy controller can be expanded to the first order around the optimal parameter values that allow perfect tracking that is when the parameters are initialized not too far from their optimal values local stability however when the set of tunable parameters is restricted to the set appearing in the linear consequent part of the rules i e the membership functions of the premises are not modified and when the reference signal is the delayed desired output the stability result is strictly valid the parameters do not have to be initialized around the perfectly tuned values in this case the algorithm can be simplified further by only considering the sign of the derivative of the output of the process in terms of its last influential input

direct adaptive fuzzy control with a self structuring algorithm this paper presents a direct self structuring adaptive fuzzy control dsafc scheme for affine nonlinear single input single output systems we show that the only restriction on the control gain is that it be positive no upper bound on this gain nor its derivative needs to be known from an initial fuzzy system with a small number of rules the self structuring algorithm adds membership functions and rules when needed to limit the size of the fuzzy system from growing indefinitely the self structuring algorithm replaces old membership functions by new ones instead of adding more membership functions so that the number of rules never exceeds a predefined upper bound the stability of the closed loop system is guaranteed using the lyapunov synthesis approach the proposed control scheme is demonstrated by application to an inverted pendulum and a magnetic levitation system

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

adaptive neural network tracking control with disturbance attenuation for multiple input nonlinear systems a switching adaptive neural network controller for multiple input nonlinear affine in the control dynamical systems with unknown nonlinearities is designed capable of arbitrarily attenuating l 2 or l infin external disturbances in the absence of disturbances a uniform ultimate boundedness property of the tracking error with respect to an arbitrarily small set around the origin is guaranteed as well as the uniform boundedness of all the signals in the closed loop the proposed switching adaptive controller effectively avoids possible division by zero while guaranteeing the continuity of switching in this way problems connected to existence of solutions and chattering phenomena are alleviated simulations illustrate the approach

mixed h 2 h control for discrete time systems via convex optimization abstract a mixed h 2 h control problem for discrete time systems is considered where an upper bound on the h 2 norm of a closed loop transfer matrix is minimized subject to an h constraint on another closed loop transfer matrix both state feedback and output feedback cases are considered it is shown that these problems are equivalent to finite dimensional convex programming problems in the state feedback case nearly optimal controllers can be chosen to be static gains in the output feedback case nearly optimal controllers can be chosen to have a structure similar to that of the central single objective h controller in particular the state dimension of nearly optimal output feedback controllers need not exceed the plant dimension

a fuzzy disturbance observer and its application to control in this paper a fuzzy disturbance observer fdo is developed and its application to the control of a nonlinear system under the internal and external disturbances is presented to construct the fdo two parameter tuning methods are proposed and shown to be useful in adjusting the parameters of the fdo the first tuning method employs the disturbance observation error to guarantee that the fdo monitors the unknown disturbance the next one enlarges the concept of error and introduces augmented error to guarantee that the fdo monitors the disturbance and the control objective is achieved in addition the relationships between the suggested fdo based control and the conventional adaptive fuzzy controls reported in the previous literatures are discussed and it is shown in a rigorous manner that the disturbance observation error or the augmented error converges to a region of which size can be kept arbitrarily small finally some examples and computer simulation results are presented to illustrate the effectiveness and the applicability of the fdo

mixed feedforward feedback based adaptive fuzzy control for a class of mimo nonlinear systems this paper proposes a mixed feedforward feedback ffb based adaptive fuzzy controller design for a class of multiple input multiple output mimo uncertain nonlinear systems by integrating both feedforward and feedback compensation we introduce the ffb based fuzzy controller composed of a feedforward fuzzy compensator and a robust error feedback compensator to achieve a forward compensation of uncertainties the feedforward fuzzy compensator takes the desired commands as premise variables of fuzzy rules and adaptively adjusts the consequent part from an error measure meanwhile the feedback controller part is constructed based on hinfin control techniques and nonlinear damping design then the attenuation of both disturbances and estimated fuzzy parametric errors is guaranteed from a linear matrix inequality lmi based gain design the main advantages are i a simpler architecture for implementation is provided and ii the typical boundedness of assumption on fuzzy universal approximation errors is not required finally an inverted pendulum system and a two link robot are taken as application examples to show the expected performance

robust stability and performance of linear time varying systems in polytopic domains a sufficient condition to assess the stability of linear time varying systems in polytopic domains is given in this paper this condition is written as a feasibility test of linear matrix inequalities expressed at the polytope vertices and taking bounds on the time derivatives of the system parameters into account differently from other techniques in the literature there is no need of gridding procedures on the parameter space neither restrictive assumptions on the uncertainty structure the proposed test can be solved in polynomial time yielding as solution a parameter dependent lyapunov function that assures the system stability moreover the results can be applied to systems with affine parameter uncertainty and can be easily extended to deal with guaranteed cost computation numerical examples show that the proposed condition can lead to less conservative evaluations of the stability domain and of the performance index for this class of systems when compared to the results based on the conventional

lmi characterization of structural and robust stability abstract this paper introduces several stability conditions for a given class of matrices expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable diagonal and simultaneous stability both characterized by polytopes of matrices are addressed using this approach a method particularly attractive to test a given matrix for d stability is proposed lyapunov parameter dependent functions are built in order to reduce conservativeness of the stability conditions the key idea is to relate hurwitz stability with a positive realness condition

h guaranteed cost control for uncertain continuous time linear systems abstract this paper deals with the h guaranteed cost control problems for continuous time uncertain systems it consist of the determination of a stabilizing state feedback gain which imposes on all possible closed loop models an h norm upper bound 0 assuming that the uncertain domain is convex bounded and the uncertain system is quadratic stabilizable with disturbance attenuation it is shown how to determine by means of a convex programming problem the global minimum of as a particular and important case for precisely known linear systems the last problem reduces to the classical h optimal control problem the results follow from the definition of a special parameter space on which the above mentioned problems are convex

brief paper an adaptive neuro fuzzy tracking control for multi input nonlinear dynamic systems an adaptive neuro fuzzy control design is suggested in this paper for tracking of nonlinear affine in the control dynamic systems with unknown nonlinearities the plant is described by a takagi sugeno t s fuzzy model where the local submodels are realized through nonlinear dynamical input output mappings our approach relies upon the effective approximation of certain terms that involve the derivative of the lyapunov function and the unknown system nonlinearities the above task is achieved locally using linear in the weights neural networks a novel resetting scheme is proposed that assures validity of the control input stability analysis provides the control law and the adaptation rules for the network weights assuring uniform ultimate boundedness of the tracking and the signals appearing in the closed loop configuration illustrative simulations highlight the approach

adaptive fuzzy controller for multivariable nonlinear state time varying delay systems subject to input nonlinearities in this paper an adaptive fuzzy variable structure controller is investigated for a class of uncertain multi input multi output mimo nonlinear time delay systems with both sector nonlinearities and dead zones a decomposition property of the control gain matrix is fully exploited in the controller design and the stability analysis the unknown time varying delay uncertainties are compensated for using an appropriate lyapunov krasovskii functional the boundedness of all signals of the closed loop system as well as the exponential convergence of the underlying tracking errors to an adjustable region are established the effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results

an lmi condition for the robust stability of uncertain continuous time linear systems a new sufficient condition for the robust stability of continuous time uncertain linear systems with convex bounded uncertainties is proposed in this note the results are based on linear matrix inequalities lmis formulated at the vertices of the uncertainty polytope which provide a parameter dependent lyapunov function that assures the stability of any matrix inside the uncertainty domain with the aid of numerical procedures based on unidimensional search and the lmis feasibility tests a simple and constructive way to compute robust stability domains can be established

neural network control of a rotating elastic manipulator abstract nonminimum phase property of a rotating elastic manipulator causes difficulties for both classical and neural network inverse model control while most of the neural network methods for control of elastic manipulators do not appear to converge to a solution when the system is lightly damped in this paper an appropriate cost function for a neural controller is proposed in the designed neural control system there are only three layer feedforward networks consisting of an input layer with two nodes one hidden layer and output layer with one node the number of units in the hidden layer and the value of the learning rate are robust to this designed network algorithm in order to simulate the transient response of the rotating elastic manipulator system a single input single output state space representation is presented for the system nonlinear model it can be seen from the simulation results the designed neural controller can not only achieve very good tracking performance zero steady state errors and strong robustness to system parameter uncertainty but also reject the effects of the input torque disturbance

fuzzy adaptive output feedback control for mimo nonlinear systems in this paper two observer based adaptive fuzzy output feedback control schemes are presented for a class of uncertain continuous time multi input multi output mimo nonlinear dynamics systems whose states are not available within these schemes fuzzy logic systems are employed to approximate the plant s unknown nonlinear functions and then the state observer is designed for estimating the states of the plant upon which a fuzzy adaptive output feedback controller is firstly investigated in order to overcome the controller singularity problem and relax the requirement of bounding parameter values a second modified fuzzy adaptive output feedback controller is proposed by using a regularized inverse and a robustifying control term all parameter adaptive laws and robustifying control terms are derived based on lyapunov stability analysis so that convergence to zero of tracking errors and boundedness of all signals in the closed loop system can be guaranteed simulations performed on a two link robot manipulator illustrate the approach and exhibit its performance

adaptive control of nonlinear systems using neural networks layered networks are used in a nonlinear adaptive control problem the plant is an unknown feedback linearizable discrete time system represented by an input output model a state space model of the plant is obtained to define the zero dynamics which are assumed to be stable a linearizing feedback control is derived in terms of some unknown nonlinear functions to identify these functions it is assumed that they can be modelled by layered neural networks the weights of the networks are updated and used to generate the control a local convergence result is given computer simulations verify the theoretical result

an improved lmi condition for robust d stability of uncertain polytopic systems a sufficient condition for robust d stability of linear systems with polytope type uncertainties is proposed the result is based on a linear parameter dependent lyapunov function obtained from the feasibility test of a set of linear matrix inequalities lmis defined at the vertices of the polytope this improved lmi condition encompasses previous results based on additional inequalities as well as results based on extra variables

a discrete time fuzzy disturbance observer and its application to control in this paper a discrete time fuzzy disturbance observer fdo is developed and its application to the control of a nonlinear system in the presence of the internal and external disturbances is presented to construct the discrete time fdo a novel tuning method is proposed and shown to be useful in adjusting the parameters of the fdo the tuning method uses the augmented error to guarantee that the fdo monitors the disturbance and the control objective is achieved the design parameters such as a learning rate used in constructing the discrete time fdo are determined in a numerical manner by solving a linear matrix inequality it is shown in a rigorous manner that both the disturbance observation error and the control error converge to a compact set of which size can be kept arbitrarily small in addition the relationships between the suggested fdo based control and the conventional adaptive fuzzy controls reported in the previous literatures are discussed finally some examples and computer simulation results are presented to illustrate the effectiveness and the applicability of the fdo

a self organizing fuzzy control approach for bank to turn missiles abstract in this paper an adaptive fuzzy autopilot is developed for bank to turn btt missiles we propose a self organizing rotated fuzzy basis function control system that is more flexible than fuzzy basis function expansion in that not only the output weights but also the shapes of fuzzy basis functions can be tuned another characteristic of this autopilot is to incorporate the terminal attractor controller into the autopilot to speed up the convergence rate the global stability analysis established in the lyapunov sense shows that the states and tracking errors of the btt missile are uniformly bounded finally there are two simulation examples to demonstrate the effectiveness of the proposed autopilot the purpose of the first example is to indicate the better performance including faster convergence speed and lower steady state error obtained by autopilots with terminal attractors as compared with that autopilot without terminal attractor another simulation result proves that btt missile can manipulate under various flight conditions in our scenarios and shows the superior tracking performance

two mode adaptive fuzzy control with approximation error estimator in this paper we propose a two mode adaptive fuzzy controller with approximation error estimator in the learning mode the controller employs some modified adaptive laws to tune the fuzzy system parameters and an approximation error estimator to compensate for the inherent approximation error in the operating mode the fuzzy system parameters are fixed only the estimator is updated online mathematically we show that the closed loop system is stable in the sense that all the variables are bounded in both modes we also establish mathematical bounds on the tracking error state vector control signal and the rms error using these bounds we show that controller s design parameters can be chosen to achieve desired control performance after that an algorithm to automatically switch the controller between two modes is presented finally simulation studies of an inverted pendulum system and a chua s chaotic circuit demonstrate the usefulness of the proposed controller

stable adaptive fuzzy control for mimo nonlinear systems in this paper an indirect adaptive fuzzy control scheme is presented for a class of multi input and multi output mimo nonlinear systems whose dynamics are poorly understood within this scheme fuzzy systems are employed to approximate the plant s unknown dynamics in order to overcome the controller singularity problem the estimated gain matrix is decomposed into the product of one diagonal matrix and two orthogonal matrices a robustifying control term is used to compensate for the lumped errors and all parameter adaptive laws and robustifying control term are derived based on lyapunov stability analysis the proposed scheme guarantees that all the signals in the resulting closed loop system are uniformly ultimately bounded uub moreover the tracking errors can be made small enough if the designed parameter is chosen to be sufficiently large a simulation example is used to demonstrate the effectiveness of the proposed control scheme

adaptive parameter estimator based on t s fuzzy models and its applications to indirect adaptive fuzzy control design in this paper a new on line parameter estimation methodology for the general continuous time takagi sugeno t s fuzzy model whose parameters are poorly known or uncertain is presented an estimator with an appropriate adaptive law for updating the parameters is designed and analyzed based on the lyapunov theory the adaptive law is designed so that the estimation model follows the parameterized plant model by the proposed estimator the parameters of the t s fuzzy model can be estimated by observing the behavior of the system and it can be a basis for indirect adaptive fuzzy control in order to show the applicability of the proposed estimator indirect adaptive fuzzy control design examples with the proposed estimator are presented

stable indirect fuzzy adaptive control this paper investigates new fuzzy model based observer adaptive control for multi input multi output continuous time nonlinear systems the proposed adaptive scheme uses takagi seguno ts fuzzy models to estimate the plant states and dynamics using stability arguments it is shown that the proposed scheme is globally asymptotically stable the observation and tracking errors are shown to converge asymptotically to zero despite the presence of external disturbances and approximation errors the performance of the developed approach is illustrated by simulation on two link robot model

stable model reference adaptive fuzzy control of a class of nonlinear systems in this paper we propose a new adaptive fuzzy control scheme called model reference adaptive fuzzy control mrafc the mrafc scheme employs a reference model to provide closed loop performance feedback for generating or modifying a fuzzy controller s knowledge base the mrafc scheme grew from ideas in conventional model reference adaptive control mrac the mrafc scheme is developed to perform adaptive feedback linearization to a class of nonlinear systems a class of fuzzy controllers which can be expressed in an explicit form is used as the primary controller based on lyapunov s second method we have developed mrafc schemes and derived fuzzy rule adaptive laws hence not only the stability of the system can be assured but also the performance such as the issues of robustness and parameter convergence of the mrafc system can be analyzed explicitly we showed that in the case of no modeling error the state error converges to zero asymptotically in the case that persistent excitation is satisfied we showed that the mrafc system is asymptotically stable by considering the periodic signal as reference input signal we showed that the square wave can make the mrafc system be persistently excited the feasibility of applying these techniques has been demonstrated by considering the control of an inverted pendulum in following a reference model response

fusion category algebras the fusion system f on a defect group p of a block b of a finite group g over a suitable p adic ring o does not in general determine the number l b of isomorphism classes of simple modules of the block we show that conjecturally the missing information should be encoded in a single second cohomology class of the constant functor with value k on the orbit category f c of f centric subgroups q of p of b which glues together the second cohomology classes q of autf q with values in k in k ulshammer puig 13 1 8 we show that if exists there is a canonical quasi hereditary k algebra f b such that alperin s weight conjecture becomes equivalent to the equality l b l f b by work of broto levi oliver 3 the existence of a classifying space of the block b is equivalent to the existence of a certain extension category l of fc by the center functor z if both invariants l exist we show that there is an o algebra l b associated with b having f b as quotient such that alperin s weight conjecture becomes again equivalent to the equality l b l l b furthermore if b has an abelian defect group l b is isomorphic to a source algebra of the brauer correspondent of b

robust static output feedback h control design for linear systems with polytopic uncertainties abstract this paper investigates the problem of robust static output feedback h control for linear systems with polytopic uncertainties a new method is proposed for robust static output feedback h controller design the proposed design method is applicable for general uncertain systems without the need to impose any constraints on system matrices the corresponding design conditions are presented in the form of linear matrix inequalities lmis one of the advantages of the new method lies in its less conservatism the proposed design method is also applicable to both continuous time and discrete time systems the performance of the method is compared with other methods based on several examples

stable adaptive control for nonlinear multivariable systems with a triangular control structure a stable adaptive controller is developed for a class of nonlinear multivariable systems using nonlinearly parametrized function approximators by utilizing the system triangular property integral type lyapunov functions are introduced for deriving the control structure and adaptive laws without the need of estimating the decoupling matrix of the multivariable nonlinear system it is shown that stability of the adaptive closed loop system is guaranteed and transient performance is analytically quantized by mean square and l sub spl infin tracking error bound criteria

brauer morphism between modular hecke algebras noticeable progress in the knowledge of modular representations of finite groups has been accomplished by considering papers of broue puig and scott the most general situations where one can define the relative traces ideal and the brauer morphism see 4 our aim in this paper is to describe what happens in the case of p permutation modules and certain derived modules most of our matter comes from unpublished results of l puig then to apply that to representations of split bn pairs in natural characteristic these two subjects have been treated previously in two papers the first one by scott 26 points out the possibility of setting up for permutation modules a theory analogous to brauer s for group algebra and which contains it the results he obtains are analogues of brauer s first and second main theorems and brauer s theorems on defect 0 and 1 the other paper by tinberg 29 presents the results of curtis and richen and sawada and green on irreducible modules for split v pairs in natural characteristic and certain associated indecomposable modules tinberg s paper contains two further results an induction formula leading to very precise information about the dimension of the involved modules and a computation of vertex the latter result using scott s paper our study of the link between these subjects permits us first to simplify part b several proofs of the curtis richen sawada theory existence of weights structure coefficients for the modular hecke algebra end indg k and after that to obtain certain results about indecomposable direct summands of indg k part c in particular we check that irreducible kc modules g is a split bn pair represented in natural characteristic are in l l correspondence with g conjugacy classes of pairs i rr where v is a p subgroup of g and 7c an irreducible kjlr v v module of defect 0

stable neural network based adaptive control for sampled data nonlinear systems for a class of mimo sampled data nonlinear systems with unknown dynamic nonlinearities a stable neural network nn based adaptive control approach which is an integration of an nn approach and the adaptive implementation of the variable structure control with a sector is developed the sampled data nonlinear system is assumed to be controllable and its state vector is available for measurement the variable structure control with a sector serves two purposes one is to force the system state to be within the state region in which the nn s are used when the system goes out of neural control and the other is to provide an additional control until the system tracking error metric is controlled inside the sector within the network approximation region the proof of a complete stability and a tracking error convergence is given and the setting of the sector and the nn parameters is discussed it is demonstrated that the asymptotic error of the system can be made dependent only on inherent network approximation errors and the frequency range of unmodeled dynamics simulation studies of a two link manipulator show the effectiveness of the proposed control approach

weights for symmetric and general linear groups abstract an important feature of the theory of finite groups is the number of connections and analogies with the theory of lie groups the concept of a weight has long been useful in the modular representation theory of finite lie groups in the defining characteristic of the group the idea of a weight in the modular representation theory of an arbitrary finite group was recently introduced in alperin proc sympos pure math 41 1987 369 379 where it was conjectured that the number of weights should equal the number of modular irreducible representations moreover this equality should hold block by block the conjecture has created great interest since its truth would have important consequences a synthesis of known results and solutions of outstanding problems in this paper we prove the conjecture first for the modular representations of symmetric groups and second for modular representations in odd characteristic r for the finite general linear groups in the latter case r may be assumed to be different from the defining characteristic p of the group since the result is known when r is p the well known analogy between the representation theory of the symmetric and general linear groups holds here too

robust model reduction of uncertain systems maintaining uncertainty structure this article presents a new approach for or robust model reduction for uncertain systems based on an optimisation algorithm applied directly in the space of reduced order model parameters the proposed approach can be applied to both polytopic or affine parameter dependent models as well as for continuous or discrete time systems the developed procedure is capable of computing both fixed reduced order model as well as uncertain reduced order model keeping the original uncertainty structure the resulting reduced order model is guaranteed to be robust stable

adaptive fuzzy control of a class of siso nonaffine nonlinear systems this paper presents a direct adaptive fuzzy control scheme for a class of uncertain continuous time single input single output siso nonaffine nonlinear dynamic systems based on the implicit function theory the existence of an ideal controller that can achieve control objectives is firstly shown since the implicit function theory guarantees only the existence of the ideal controller and does not provide a way for constructing it a fuzzy system is employed to approximate this unknown ideal control law the adjustable parameters in the used fuzzy system are updated using a gradient descent adaptation algorithm this algorithm is designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the used fuzzy control law the stability analysis of the closed loop system is performed using a lyapunov approach in particular it is shown that the tracking error converges to a neighborhood of zero the effectiveness of the proposed adaptive control scheme is demonstrated through the simulation of a simple nonaffine nonlinear system

adaptive control of a class of nonlinear systems with fuzzy logic an adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture employs fuzzy systems which are expressed as a series expansion of basis functions to adaptively compensate for the plant nonlinearities global asymptotic stability of the algorithm is established in the lyapunov sense with tracking errors converging to a neighborhood of zero simulation results for an unstable nonlinear plant are included to demonstrate that incorporating the linguistic fuzzy information from human experts results in superior tracking performance

h tracking based adaptive fuzzy neural control for mimo uncertain robotic systems with time delays in this paper a novel adaptive fuzzy neural control afnc scheme for multi input multi output uncertain robotic systems is proposed for h tracking performance and to suppress the effects caused by multiple time delayed state uncertainties unmodeled dynamics and disturbances each delayed uncertainty is assumed to be bounded by an unknown gain a reference model with the desired amplitude and phase properties is given to construct an error model a fuzzy neural fn system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors the proposed afnc scheme uses two on line estimations which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the fn system simultaneously stability and robustness of the afnc scheme is analyzed in lyapunov sense it is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed loop system with h tracking performance for the overall system without a priori knowledge on the upper bounds of the delayed state uncertainties the performance of the proposed scheme is evaluated through the simulation results simulations are given to show the validity and confirm the performance of the proposed scheme

adaptive fuzzy control of a class of mimo nonlinear systems this paper presents two indirect adaptive fuzzy control schemes for a class of uncertain continuous time multi input multi output nonlinear dynamic systems within these schemes fuzzy systems are employed to approximate the plant s unknown nonlinear functions and robustifying control terms are used to compensate for approximation errors by using a regularized matrix inverse a stable well defined adaptive controller is firstly investigated then in order to obtain an adaptive controller not depending upon any parameter initialization conditions and to relax the requirement of bounding parameter values a second adaptive controller is proposed all parameter adaptive laws and robustifying control terms are derived based on lyapunov stability analysis so that under appropriate assumptions semi global stability and asymptotic convergence to zero of tracking errors can be guaranteed simulations performed on a two link robot manipulator illustrate the approach and exhibit its performance

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

observer based fuzzy adaptive control for strict feedback nonlinear systems in this paper a new fuzzy adaptive control approach is developed for a class of siso strict feedback nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is introduced for state estimation as well as system identification under the framework of the backstepping design fuzzy adaptive output feedback control is constructed recursively it is proven that the proposed fuzzy adaptive control approach guarantees the semi global boundedness property for all the signals and the tracking error to a small neighborhood of the origin simulation studies are included to illustrate the effectiveness of the proposed approach

perspectives of fuzzy systems and control although fuzzy control was initially introduced as a model free control design method based on the knowledge of a human operator current research is almost exclusively devoted to model based fuzzy control methods that can guarantee stability and robustness of the closed loop system state of the art techniques for identifying fuzzy models and designing model based controllers are reviewed in this article attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy such as expert control supervision and diagnostic systems open issues are highlighted and an attempt is made to give some directions for future research

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

stable multi input multi output adaptive fuzzy neural control in this letter stable direct and indirect adaptive controllers are presented that use takagi sugeno t s fuzzy systems 1985 conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi input multi output mimo square nonlinear plants with poorly understood dynamics the direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics we prove that with or without such knowledge the adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of the reference inputs we do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero

feedback linearization using neural networks abstract for a class of single input single output continuous time nonlinear systems a multilayer neural network based controller that feedback linearizes the system is presented control action is used to achieve tracking performance for a state feedback linearizable but unknown nonlinear system the control structure consists of a feedback linearization portion provided by two neural networks plus a robustifying portion that keeps the control magniture bounded a stability proof is given in the sense of lyapunov it is shown that all the signals in the closed loop system are uniformly ultimately bounded no off line learning phase is needed initialization of the network weights is straightforward

robust h performance using lifted polynomial parameter dependent lyapunov functions this paper investigates the robust h performance of time invariant linear uncertain systems where the uncertainty is in polytopic domains robust h is checked by constructing a quadratic parameter dependent lyapunov function the matrix associated with this quadratic lyapunov function is a polynomial function of the uncertain parameters expressed as a particular polynomial matrix involving powers of the dynamic matrix of the system and one symmetric matrix to be determined the degree of this polynomial matrix function is arbitrary finsler s lemma is used to lift the obtained stability conditions into a larger space in which sufficient stability tests can be developed in the form of linear matrix inequalities as increases less conservative h evaluations are obtained both continuous and discrete time systems are investigated numerical examples illustrate the method and compare the present results with similar works in the literature

a parameter dependent lyapunov function for a polytope of matrices a new sufficient condition for a polytope of matrices to be hurwitz stable is presented the stability is a consequence of the existence of a parameter dependent quadratic lyapunov function which is assured by a certain linear constraint for generating extreme matrices of the polytope the condition can be regarded as a duality of the known extreme point result on quadratic stability of matrix polytopes where a fixed quadratic lyapunov function plays the role the obtained results are applied to a polytope of second degree polynomials for illustration

parameter and controller dependent lyapunov functions for robust d stability and robust performance controller design this paper addresses the design of output controllers of chosen order in a given set for ensuring a number of desired properties such as robust d stability and robust performance it is shown that a sufficient condition for determining such controllers can be obtained by solving convex optimization problems with linear matrix inequality constraints through the introduction of a lyapunov function depending polynomially on both uncertainty and controller the proposed condition is also necessary for sufficiently large degrees of the polynomials involved under some assumptions

observer based fuzzy adaptive control for multi input multi output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction in this study we present an observer based fuzzy adaptive control scheme for a class of uncertain multi input multi output nonlinear systems with a nonsymmetric control gain matrix unknown control direction and unmeasured states in this scheme fuzzy systems are used to approximate the unknown nonlinear functions and an adaptive fuzzy state observer is designed to estimate the unmeasured states the parameter adaptive laws are designed by fuzzy basis functions rather than by its filtering and a robust control term is used to compensate for the lumped errors the proposed method solves the problem of the nonsymmetric control gain matrix and it requires no a priori knowledge of the control direction for the states that are unmeasured we prove that all of the signals in the resulting closed loop systems are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

a new robust d stability condition for real convex polytopic uncertainty abstract the problem of robust d stability analysis with respect to real convex polytopic uncertainties is tackled a new lmi based sufficient condition for the existence of parameter dependent lyapunov functions is proposed this condition generalises previously published conditions numerical comparisons with quadratic stability results as well as previous results based on parameter dependent lyapunov functions illustrate the relevance of this new condition finally this result appears to be promising for robust multi objective performance analysis and control synthesis purposes

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

robust neuro fuzzy control of multivariable systems by tuning consequent membership functions a robust neuro fuzzy controller with tuning mechanism of membership functions and neural weights to achieve the tracking control of composite multivariable systems is proposed the control strategy is developed to facilitate robust property by self tuning the consequent membership functions of the fuzzy controllers by an on line tuning mechanism the fuzzy system can effectively deal with the equivalent uncertainties that may appear in the subsystems due to plant uncertainty function approximation error or external disturbance by using lyapunov stability theory the overall system with the proposed controller has been proved to be uniform ultimate bounded simulation results of a two link robot control demonstrate the effectiveness and robustness of the design

h guaranteed cost computation by means of parameter dependent lyapunov functions a linear matrix inequality approach to compute h guaranteed costs by means of parameter dependent lyapunov functions is presented in this paper the uncertain linear time invariant systems are supposed to belong to convex bounded domains polytope type uncertainty the conditions proposed are less conservative than other parameter dependent based methods from the literature providing better estimates of worst case h norms in both continuous and discrete time systems as illustrated by means of numerical examples

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

h sub 2 h sub spl infin filter design for systems with polytope bounded uncertainty this correspondence presents a strategy for robust h2 h infin filtering design with regional pole placement applied to discrete or continuous time linear time invariant lti systems with polytope bounded uncertainty to overcome the conservatism of linear matrix inequality lmi based formulations the proposed design approach is based on a multiobjective optimization algorithm applied directly in the space of the filter parameters the h2 and hinfin norms computed in all polytope vertices and in possible worst case interior points are taken as the optimization objectives a combination of branch and bound algorithm and lmi guaranteed cost formulations is applied to compute the coordinates of the worst case norms and to validate the filter design to the whole polytope examples are presented to illustrate the effectiveness of the proposed strategy

fuzzy model reference adaptive control this paper investigates a fuzzy model reference adaptive controller fmrac for continuous time multiple input multiple output mimo nonlinear systems the proposed adaptive scheme uses a takagi seguno ts fuzzy adaptive system which allows for the inclusion of a priori information in terms of qualitative knowledge about the plant operating points or analytical regulators e g state feedback for those operating points a proportional integral update law is used to obtain a fast parameters adaptation stability and robustness of this adaptive scheme are established using lyapunov stability tools the simulation results for a two link robot confirm the performance of the proposed approach

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

stable adaptive neuro control design via lyapunov function derivative estimation a new approach to the tracking problem for affine in the control nonlinear dynamical systems whose nonlinearities are assumed to be unknown is presented in this paper the philosophy of the developed technique is based on estimating the derivative of an unknown lyapunov function exploiting the approximation capabilities of the linear in the weights neural network structures a novel resetting strategy guarantees the boundedness away from zero of certain signals the uniform ultimate boundedness of the tracking error to an arbitrarily small set plus the boundedness of all other signals in the closed loop is guaranteed

dynamic structure adaptive neural fuzzy control for mimo uncertain nonlinear systems this paper proposes a novel dynamic structure neural fuzzy network dsnfn to address the adaptive tracking problems of multiple input multiple output mimo uncertain nonlinear systems the proposed control scheme uses a four layer neural fuzzy network nfn to estimate system uncertainties online the main feature of this dsnfn is that it can either increase or decrease the number of fuzzy rules over time based on tracking errors projection type adaptation laws for the network parameters are derived from the lyapunov synthesis approach to ensure network convergence and stable control a hybrid control scheme that combines the sliding mode control and the adaptive bound estimation control with different weights improves system performance by suppressing the influence of external disturbances and approximation errors as the employment of the dsnfn high quality tracking performance could be achieved in the system furthermore the trained network avoids the problems of overfitting and underfitting simulations performed on a two link robot manipulator demonstrate the effectiveness of the proposed control scheme

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

adaptive tuning of the fuzzy controller for robots an adaptive tuning algorithm of the fuzzy controller is developed for a class of serial link robot arms the algorithm can on line tune parameters of premise and consequence parts of fuzzy rules of the fuzzy basis function fbf controller the main part of the fuzzy controller is a fuzzy basis function network to approximate unknown rigid serial link robot dynamics under some mild assumptions a stability analysis guarantees that both tracking errors and parameter estimate errors are bounded moreover a robust technique is adopted to deal with uncertainties including approximation errors and external disturbances simulations of the proposed controller on the puma 560 robot arm demonstrate the effectiveness

technical communique establishing tightness in robust h analysis via homogeneous parameter dependent lyapunov functions several methods have been proposed to provide upper bounds to the robust h performance of a linear system with polytopic state space uncertainty a common problem of these methods is the lack of a test for establishing if the found upper bound is tight or not which is essential to determine if the search of the sought performance is finished or should continue this paper provides a necessary and sufficient condition for establishing the tightness of the upper bound provided by homogeneous polynomially parameter dependent quadratic lyapunov functions hpd qlfs which recently have been shown to be a powerful tool for computing these upper bounds this condition is based on the existence of particular vectors in suitable linear spaces techniques for finding these vectors are also provided

fuzzy adaptive controller for mimo nonlinear systems with known and unknown control direction this paper investigates fuzzy adaptive control schemes for a class of multi input multi output mimo unknown nonlinear systems with known and unknown sign of the control gain matrix three fuzzy adaptive control schemes are developed in the design of the second and third controller we will exploit a decomposition of the control gain matrix into a symmetric positive definite matrix a diagonal matrix with diagonal entries 1 or 1 and a unity upper triangular matrix the nussbaum type function is used to deal with the unknown control direction i e the unknown sign of the control gain matrix for updating the parameters of the fuzzy system an adaptation proportional integral pi law is proposed theoretical results are illustrated through two simulation examples

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

lpv control and full block multipliers a novel construction of linear parameter varying controllers is presented for arbitrarily fast parameter variations it is shown how full block multipliers allow to considerably reduce conservatism various auxiliary results of independent interest are included

adaptive fuzzy control for mimo nonlinear systems with nonsymmetric control gain matrix and unknown control direction in this paper an indirect adaptive fuzzy control scheme is developed for a class of uncertain multi input multi output nonlinear systems with nonsymmetric control gain matrix and unknown control direction the nonsymmetric control gain matrix is expressed as the sum of a symmetric matrix and a skew symmetric matrix and the symmetric matrix as well as the skew symmetric matrix is approximated by fuzzy systems by using the symmetric matrix decomposition technique the estimated symmetric matrix is decomposed into the product of one diagonal matrix and two orthogonal matrixes based on the decomposition results the adaptive fuzzy controller is developed to avoid the possible singularity problem and the parameter initialization problem a robust control term is employed to compensate for the lumped errors and a nussbaum type function is incorporated in the robust control term to deal with the unknown control direction the proposed scheme guarantees that all the signals in the resulting closed loop system are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

ℋ2 guaranteed cost control for uncertain discrete time linear systems the 2 guaranteed cost control problem is analysed for uncertain discrete time linear systems it consists on the determination of a constant state feedback stabilizing matrix gain and an 2 norm upper bound which holds for all feasible models two different approaches are considered the first is based on the optimality conditions provided by bellmans s dynamic programming equation the second is based on the geometric properties of the aforementioned problem it is shown that it is possible to parametrize all stabilizing gains over a convex set in this special parameter space the 2 cost is found to be a linear function of the free parameters finally some relationships between these approaches are presented and numerical examples given