ekf based enhanced performance controller design for nonlinear stochastic systems in this paper a novel control algorithm is presented to enhance the performance of the tracking property for a class of nonlinear and dynamic stochastic systems subjected to non gaussian noises although the existing standard pi controller can be used to obtain the basic tracking of the systems the desired tracking performance of the stochastic systems is difficult to achieve due to the random noises to improve the tracking performance an enhanced performance loop is constructed using the ekf based state estimates without changing the existing closed loop with a pi controller meanwhile the gain of the enhanced performance loop can be obtained based upon the entropy optimization of the tracking error in addition the stability of the closed loop system is analyzed in the mean square sense the simulation results are given to illustrate the effectiveness of the proposed control algorithm

h sub infinity optimal control with state feedback a h sub infinity optimal control problem in which the measured outputs are the states of the plant is considered the main result shows that the infimum of the norm of the closed loop transfer function using linear static state feedback equals the infimum of the norm of the closed loop transfer function over all stabilizing dynamic even nonlinear time varying state feedback controllers

convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled data systems under dwell time constraints stability analysis and control of linear impulsive systems is addressed in a hybrid framework through the use of continuous time time varying discontinuous lyapunov functions necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas extensions to the stability of aperiodic systems under minimum maximum and ranged dwell times are then derived by exploiting further the particular structure of the stability conditions the results are non conservatively extended to quadratic stability analysis of linear uncertain impulsive systems these stability criteria are in turn losslessly extended to stabilization using a particular yet broad enough class of state feedback controllers providing then a convex solution to the open problem of robust dwell time stabilization of impulsive systems using hybrid stability criteria relying finally on the representability of sampled data systems as impulsive systems the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled data systems are straightforwardly solved using the same ideas several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach

polynomial filtering for linear discrete time non gaussian systems in this work we propose a new filtering approach for linear discrete time non gaussian systems that generalizes a previous result concerning quadratic filtering a de santis a germani and m raimondi ieee trans automat control 40 1995 pp 1274 1278 a recursive nu th order polynomial estimate of finite memory delta is achieved by defining a suitable extended state which allows one to solve the filtering problem via the classical kalman linear scheme the resulting estimate will be the mean square optimal one among those estimators that take into account nu polynomials of the last delta observations numerical simulations show the effectiveness of the proposed method

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

comments on stability margin evaluation for uncertain linear systems the bound derived in the above paper by gong thompson ibid vol 39 no 3 p 548 50 1994 is shown via two new stability criteria not to be the tightest possible for all unstructured perturbations a minor error of their theorem is also corrected

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

stability and performance in the presence of magnitude bounded real uncertainty riccati equation based state space approaches abstract this paper is concerned with riccati equation based analysis methods for determining stability and performance of perturbed feedback systems the elements of the state space representation of the systems are assumed to be linearly perturbed with real magnitude bounded uncertaintites performance is defined as the value of the h norm of the transfer function of interest an analysis method based on checking the existence of a common solution to a finite set of riccati inequalities is proposed it represents a nonconvex optimization problem this problem is then transformed into a convex optimization problem by the use of properties of certain matrix inequalities

stabilizing controllers for bilinear systems the problem of finding stabilizing feedback controllers for continuous bilinear systems where the controls act additively and multiplicatively simultaneously is treated the applicability of the quadratic control law of jacobson 5 and others is extended to the case when the a matrix has arbitary eigenvalues under certain conditions a class of bilinear systems common among biochemical flow systems is defined the dyadic bilinear systems a control scheme the so called division controller for dyadic bilinear systems is suggested the practicality of the control schemes is demonstrated on the problem of controlling the neutron level in a fission reactor

on the stabilization of the homogeneous bilinear systems abstract the problem of stabilizing the single input homogeneous bilinear systems is considered a special class of these systems is considered the matrix of the linear i e control independent term of the right hand side is semitable while the matrix of the bilinear term is skew symmetric two types of stabilization are investigated constant feedback global asymptotic stabilization and practical stabilization by a family of the linear feedbacks it will be shown for the planar case that the above system is always practically stabilizable by a family of the linear feedbacks for n 3 the solution of both stabilization problems depends on the mutual position of the expanding direction of the linear part and the direction of the infinitesimal rotation defined by the bilinear term

notions of stabilizability and controllability for a class of uncertain linear systems abstract this paper investigates the relationship between stabilizability and certain notions of controllability for a class of uncertain linear systems containing time varying unknown but bounded uncertain parameters the paper introduces a notion of controllability invariance roughly speaking an uncertain system is controllability invariant if it is controllable in the usual sense for each fixed value of the uncertain parameters the paper describes a class of uncertain systems for which controllability invariance implies stabilizability

global asymptotic stability analysis of discrete time cohen grossberg neural networks based on interval systems abstract the global asymptotic stability of discrete time cohen grossberg neural networks cgnns with or without time delays is studied in this paper the cgnns are transformed into discrete time interval systems and several sufficient conditions for asymptotic stability for these interval systems are derived by constructing some suitable lyapunov functionals the conditions obtained are given in the form of linear matrix inequalities that can be checked numerically and very efficiently by using the matlab lmi control toolbox finally some illustrative numerical examples are provided to demonstrate the effectiveness of the results obtained

robust control of linear systems with generalized positive real uncertainty abstract this paper focuses on linear systems subjected to a new class of time varying parameter uncertainty the parameter uncertainty under consideration generalizes both positive real and norm bounded uncertainty in some sense and is a more realistic description of uncertainty for many practical systems the problems of robust stability analysis robust stabilization and robust h control for this class of uncertain systems are studied it is shown that the above robust control problems can be converted into associated scaled h control ones

nonlinear bounded control for norm bounded uncertain systems in this paper a method to derive a bounded continuous feedback control function which stabilizes a norm bounded uncertain linear system in a certain region is proposed the aim is to ensure a certain performance level in a neighborhood ellipsoid of the origin through a guaranteed cost state feedback control outside this neighborhood a linear like control with state dependent gains is obtained from the solutions of a family of parameter dependent algebraic riccati equation similar to the one arising in h sub spl infin control

on robust and h controls for a class of linear and bilinear systems with nonlinear uncertainty this paper is concerned with robust stabilization for linear and bilinear systems with nonlinear uncertainty by using quadratic lyapunov functions our controls guarantee the uniform exponential stability of uncertain systems moreover the controls have a simple structure and are easily handled some problems of h control for these systems are also considered 1997 elsevier science ltd

robust stabilization of linear systems with norm bounded time varying uncertainty abstract in this paper robust stabilization of a class of linear systems with norm bounded time varying uncertainties is considered it is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a parameter dependent riccati equation also a construction for the stabilizing feedback law is given in terms of the solution to the riccati equation

robustness of controllability and observability of continuous linear time varying systems with parameter perturbations the controllability and the observability of continuous linear time varying systems with norm bounded parameter perturbations are analyzed the sufficient conditions which ensure the controllability of the perturbed system are presented by using the derived state transition matrix relationship between the nominal system and the perturbed system the proposed sufficient conditions allow the evaluation of controllability under the norm bounded parameter perturbations the robustness of the observability is also studied for continuous linear time varying systems with norm bounded parameter perturbations and the corresponding sufficient conditions are provided

hybrid filtering for linear systems with non gaussian disturbances this paper is concerned with hybrid filtering of a non gaussian system coupled by a hidden switching process an optimal control approach is used to derive a finite dimensional recursive filter that is optimal in the sense of the most probable trajectory mpt estimate an approximate scheme is obtained when the probability distribution of the switching process converges to a limiting distribution which is often easier to obtain numerical examples are considered and computational experiments are reported in these examples our schemes outperform popular filtering schemes available in the literature

parametric quadratic stabilizability of uncertain nonlinear systems abstract the objective of this paper is to introduce the notion of parametric quadratic stabilizability pq stabilizability of nonlinear control systems x a a p x b p u when we consider nonlinear systems reference inputs and disturbances may alter dynamics in an essential way by moving the equilibrium to a new location or destroying it altogether for this reason when we consider quadratic stabilizability q stabilizability of nonlinear systems we need to combine the two concepts of parametric stability and q stabilizability and consider pq stabilizability when nonlinear function belongs to a subclass of passive functions it is shown that the necessary and sufficient condition for quadratic stabilizability q stabilizability of linear systems via dynamic state feedback which was derived by zhou and khargonekar is also a necessary and sufficient condition for that of nonlinear systems considered in this paper moreover when nonlinear function belongs to a subclass of incresing functions and when b 0 it shown that the necessary and sufficient condition for q stabilizability of linear systems via static state feedback which was derrived by petersen is also a necessary and sufficient condition for that of nonlinear systems considered in this paper

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

a unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback we study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties our approach relies on well known h sub spl infin linear control tools and allows one to recover and improve in the unifying framework of a semiglobal separation result existing results on the semiglobal stabilization via output feedback in particular we discuss the case of uncorrupted outputs input and output nonlinearities or model uncertainties which may include for example practical situations such as backlash hysteresis and saturations the key feature of our design procedure is given by the choice of two continuous functions the first one is instrumental in constructing a stabilizing controller the second one arises in the candidate lyapunov function for the closed loop system relying on our main theorem we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems

passivity analysis and passification for uncertain signal processing systems the problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers decision feedback equalizers and digital and analog filters equally important is the problem of passification where a compensator needs to be designed for a given system to become passive this paper considers these two problems for a large class of systems that involve uncertain parameters time delays quantization errors and unmodeled high order dynamics by characterizing these and many other types of uncertainty using a general tool called integral quadratic constraints iqcs we present solutions to the problems of robust passivity analysis and robust passification more specifically for the analysis problem we determine if a given uncertain system is passive for all admissible uncertainty satisfying the iqcs similarly for the problem of robust passification we are concerned with finding a loop transformation such that a particular part of the uncertain signal processing system becomes passive for all admissible uncertainty the solutions are given in terms of the feasibility of one or more linear matrix inequalities lmis which can be solved efficiently

a generalization of the routh hurwitz stability criteria and an application to a problem in robust controller design the classical results of routh and hurwitz on the stability of polynomials are generalized from the open left half plane to certain other subregions g of the complex plane by our method arbitrary conic sections can be handled the results are interpreted as criteria for g stability of linear systems a numerical algorithm to compute the criteria is given an application to a problem in robust controller design is outlined

minimum entropy control of closed loop tracking errors for dynamic stochastic systems the entropy has been used to characterize the uncertainty of the tracking error for general nonlinear and non gaussian stochastic systems a recursive optimization solution has been developed and the local stability condition of the closed loop system has been established the generality of this algorithm has been proved by the special case study of the minimum variance control for linear gaussian systems

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

observer based feedback controller design for a class of stochastic systems with non gaussian variables in this note the observer based feedback control problem is investigated for a class of non gaussian stochastic systems the proposed control strategy is the optimal control under a performance function measuring a sort of entropy of the state deviation sufficient conditions under which the closed loop system is locally and ultimately bounded in the mean square sense are presented simulation results demonstrate the effectiveness of the proposed design method

robust stability and performance of stochastic uncertain systems on an infinite time interval abstract in this paper we consider a robust stability problem for continuous time stochastic uncertain systems the uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input this uncertainty is assumed to satisfy a certain relative entropy constraint the solution to a specially parametrized risk sensitive performance analysis problem is used to estimate the level of guaranteed performance for the stochastic uncertain system under consideration this solution is obtained by solving an algebraic riccati equation the corresponding performance bound holds for all admissible uncertainties and is nonconservative

robust schur stability of a polytope of polynomials the main objective of the authors is to provide a necessary and sufficient condition for a polytope of polynomials to have all its zeros inside the unit circle the criterion obtained serves as a discrete time counterpart for results in s bialas 1985 and f fu and b r barmish 1987 for the continuous case also the results are reduced to operations on n 1 n 1 matrices it is concluded that by the edge result of a c bartlett et al 1987 it suffices to check the exposed edges in order to determine whether a polytope of polynomials has all its zeros in a simply connected region d

stabilization of uncertain systems with norm bounded uncertainty a control a robust stabilization problem in a state space setting is treated it is assumed that the states are available for feedback using a fixed lyapunov function approach quadratic stability it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state feedback controller as a consequence it is shown that the existence of a quadratically stabilizing nonlinear time varying dynamic state feedback controller implies the existence of a quadratically stabilizing memoryless linear time invariant state feedback compensator

stabilization of an uncertain linear system in which uncertain parameters enter into the input matrix this paper presents a procedure for stabilizing a class of uncertain linear systems the uncertain systems under consideration are described by state equations in which the input matrix depends on a matrix of uncertain parameters this matrix of uncertain parameters may be time varying however it is constrained by a bound on its induced norm the stabilization procedure presented involves the repeated solution of an algebraic riccati equation when a positive definite solution to this riccati equation is obtained this solution is used to construct a stabilizing linear control law another important result contained in this paper can be stated roughly as follows for the class of uncertain systems under consideration if a system can be stabilized via nonlinear control then it is also possible to stabilize the system via linear control

the constrained lyapunov problem and its application to robust output feedback stabilization given a dynamical system whose description includes time varying uncertain parameters it is often desirable to design an output feedback controller leading to asymptotic stability of a given equilibrium point when designing such a controller one may consider static i e memoryless or dynamic compensation in this paper we show that solvability of various output feedback design problems is implied by existence of a solution to a certain constrained lyapunov problem clp the clp can be stated in purely algebraic terms once the clp is described we provide necessary and sufficient conditions for its solution to exist subsequently we consider application of the clp to a number of robust stabilization problems involving static output feedback and observer based feedback

almost sure stabilization of uncertain continuous time markov jump linear systems this work deals with the robust almost sure as stabilization problem for continuous time markov jump linear systems mjls norm bounded uncertainties affecting the system state and input matrices are considered a deterministically testable sufficient condition for robust as stability is provided which relies on a bound on the 2 norm of the system transition matrix such a condition can be profitably employed also to design a robust feedback stabilization strategy such feedback design is based on a formulation of the sufficient condition for robust as stability in terms of an equivalent lmi problem

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

turner doubles and generalized schur algebras abstract turner s conjecture describes all blocks of symmetric groups and hecke algebras up to derived equivalence in terms of certain double algebras with a view towards a proof of this conjecture we develop a general theory of turner doubles in particular we describe doubles as explicit maximal symmetric subalgebras of certain generalized schur algebras and establish a schur weyl duality with wreath product algebras

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

brief paper optimal probability density function control for narmax stochastic systems this paper presents a new control strategy for a class of non gaussian stochastic systems so that the output probability density function pdf of the system can be made to follow a desired pdf the system considered is represented by an nonlinear autoregressive and moving average with exogenous narmax inputs with input channel time delay and non gaussian noise a multi step ahead nonlinear cumulative cost function is used to improve tracking performance for this purpose a relationship between the pdfs of all the inputs and the pdfs of multiple step ahead output is formulated by constructing an auxiliary multivariate mapping by minimizing this performance function a new explicit predictive controller design algorithm is established with less conservatism than some previous results furthermore an improved approach is developed to guarantee the local stability of the closed loop system by tuning the weighting parameters recursively simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained

brief robust stabilization and guaranteed cost control for discrete time linear systems by static output feedback this paper proposes a systematic approach for the static output feedback control design for discrete time uncertain linear systems it is shown that if the open loop system satisfies some particular structural conditions and the uncertainty has a specific structure a static output feedback gain can be calculated easily using a formula only involving the original system matrices among the conditions the system has to satisfy the strongest one relies on a minimum phase argument square and nonsquare systems are considered the performance problem through a quadratic criterion is also discussed guaranteed cost control

based quasi hereditary algebras abstract a notion of a split quasi hereditary algebra has been defined by cline parshall and scott du and rui describe a based approach to split quasi hereditary algebras we develop this approach further to show that over a complete local noetherian ring one can achieve even stronger basis properties this is important for schurifying quasi hereditary algebras as developed in our subsequent work the schurification procedure associates to an algebra a a new algebra which is the classical schur algebra if a is a field schurification produces interesting new quasi hereditary and cellular algebras it is important to work over an integral domain of characteristic zero taking into account a super structure on the input algebra a so we pay attention to super structures on quasi hereditary algebras and investigate a subtle conforming property of heredity data which is crucial to guarantee that the schurification of a is quasi hereditary if so is a we establish a morita equivalence result which allows us to pass to basic quasi hereditary algebras preserving conformity

optimal guaranteed cost control of uncertain discrete time delay systems this paper considers the problem of robust guaranteed cost control of linear discrete time delay systems with parametric uncertainties by matrix inequality approach the robust quadratic stability of the system is studied a control design method is developed such that the closed loop system with a cost function has a upper bound irrespective of all admissible parameter uncertainties and unknown time delays furthermore the upper bound cost can be optimized by incorporating with a minimization problem a numerical example is given to show the potential of the proposed techniques

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

an implicit small gain condition and an upper bound for the real structured singular value in this paper we develop an upper bound for the real structured singular value that has the form of an implicit small gain theorem the implicit small gain condition involves a shifted plant whose dynamics depend upon the uncertainty set bound and unlike prior bounds does not require frequency dependent scales or multipliers numerical results show that the implicit small gain bound compares favorably with real bounds that involve frequency dependent scales and multipliers

minimum entropy filtering for multivariate stochastic systems with non gaussian noises in this note a minimum entropy filtering algorithm is presented for a class of multivariate dynamic stochastic systems which are represented by a set of time varying difference equations and are subjected to the multivariate non gaussian stochastic inputs several new concepts including the hybrid random vector hybrid probability and hybrid entropy are firstly established to describe the probabilistic property of the estimation errors new relationships are provided between the probability density functions pdfs of the multivariate stochastic input and output for different mapping cases recursive algorithms are then proposed to design the real time sub optimal filter so that the hybrid entropy of the estimation error can be minimized finally an improved algorithm is provided through the on line tuning of the weighting matrices so as to guarantee the local stability of the error system

brief paper distribution function tracking filter design using hybrid characteristic functions a new tracking filtering algorithm for a class of multivariate dynamic stochastic systems is presented the system is expressed by a set of time varying discrete systems with non gaussian stochastic input and nonlinear output a new concept such as hybrid characteristic function is introduced to describe the stochastic nature of the dynamic conditional estimation errors where the key idea is to ensure the distribution of the conditional estimation error to follow a target distribution for this purpose the relationships between the hybrid characteristic functions of the multivariate stochastic input and the outputs and the properties of the hybrid characteristic function are established a new performance index of the tracking filter is then constructed based on the form of the hybrid characteristic function of the conditional estimation error an analytical solution which guarantees the filter gain matrix to be an optimal one is then obtained a simulation case study is included to show the effectiveness of the proposed algorithm and encouraging results have been obtained

effects of using observers on stabilization of uncertain linear systems the effects of observers on robust linear feedback controllers are studied sufficient conditions are obtained that guarantee full recovery of the allowable uncertainty bounds attainable by full state feedback the effects of the resulting high gain observers on the disturbance rejection bounds are also studied it is shown that full recovery of the uncertainty bound leads to possible large degradation in disturbance rejection however if there is only additive plant disturbance and no measurement disturbance this degradation can be prevented

static output feedback fuzzy controller for chen s chaotic system with uncertainties static output feedback stabilization of chen s chaotic system with uncertainties is studied from a fuzzy control approach an uncertain takagi sugeno ts fuzzy model for the uncertain chen s chaotic system is first constructed then the uncertain ts fuzzy model is represented as a set of uncertain linear systems and a controller design algorithm is proposed specifically a switching static output feedback fuzzy model based controller is designed by solving some linear matrix inequalities lmi which are derived from the developed local representations simulation results have confirmed the effectiveness and feasibility of the proposed modeling and control methods

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

exact calculation of the multiloop stability margin a mapping theorem by l a zadeh and c a desoer 1963 serves as the basis for an algorithm that computes the stability margin k sub m of diagonally perturbed multivariable feedback systems without conservatism the stability margin determination not only verifies system stability but also quantifies how much further the plan uncertainties can be extended before instability occurs the essence of the computational approach is the realization that the true image of a given domain can be approximated with arbitrary accuracy by first subdividing the domain into the requisite number of subdomains and then forming the union of the convex hulls of their images the technique is illustrated in an example with a plant model having three uncertainties in general the method is applicable to either siso or mimo lti systems whose uncertainties can be modeled with noninteracting coefficients in the open loop transfer function representations

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

an approach to h control of a class of nonlinear systems this paper considers robust h control of a class of nonlinear systems that can be represented by a heterogeneous model a new controller design method using both state feedback is proposed based on quadratic stability theory a number of necessary and sufficient conditions are derived for quadratic stabilizability with disturbance attenuation of the control system concerned an example is also given to demonstrate the performance of the proposed controller design methods

an algebraic approach to robust h control via state feedback abstract this paper considers the problem of robust h control design for linear uncertain systems we show that for a certain type of time varying norm bounded parameter uncertainty the problem is equivalent to an h control problem therefore a complete solution is achieved by using the existing results of h control theory the paper presents a state feedback design which stabilizes the plant for all admissible uncertainties and also guarantees a prescribed level of disturbance attenuation in a certain sense

absolute stability of systems under block diagonal memoryless uncertainties abstract absolute stability of systems under block diagonal uncertainties is studied a quadratic lyapunov function is used it is found that the quadratic stability condition of such a system is equivalent to that of systems with uncertainties restricted to be rank one matrices the main technique used is exact penalization in nonsmooth analysis

the algorithms for studying the trade offs between h attenuation and uncertainty tolerance uncertainty tolerance and h attenuations are two important concerns in feedback control design it is therefore important to develop effective methods to compute the trade off between these two objectives using a quasiconvex optimization approach this paper develops algorithms for two problems in this regard 1 given the uncertainty size of the system compute the minimum h norm bound of the closed loop system reachable by state feedback control and 2 given the required maximum acceptable h norm bound of the closed loop system compute the maximum uncertainty size which can be tolerated when state feedback control is applied a numerical example is included to show the trade off between uncertainty tolerance and h attenuations and the effectiveness of the algorithms

technical communique on the existence of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties recently choi 1998 automatica 34 8 1015 1020 has considered the problem of designing a variable structure control vsc law for uncertain systems where the uncertainty in the state model does not satisfy the matching condition he has given a sufficient condition for the existence of linear sliding surfaces in terms of lmis in this note we show that the lmi existence condition given in the above paper is a necessary and sufficient one and we give lmi existence conditions of a sliding surface guaranteeing general lmi regional pole placement constraints while in the above paper pole placement only in a vertical half plane and a disk has been considered finally we give simulation results for controlling an inverted pendulum mounted on a cart

robust filtering for a class of stochastic uncertain nonlinear time delay systems via exponential state estimation we investigate the robust filter design problem for a class of nonlinear time delay stochastic systems the system under study involves stochastics unknown state time delay parameter uncertainties and unknown nonlinear disturbances which are all often encountered in practice and the sources of instability the aim of this problem is to design a linear delayless uncertainty independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances the dynamics of the estimation error is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are proposed to guarantee the existence of desired robust exponential filters which are derived in terms of the solutions to algebraic riccati inequalities the developed theory is illustrated by numerical simulation

h optimal sampled data control in continuous time systems we consider the design of h optimal discrete time digital controllers in continuous time systems an apparent difficulty especially in utilizing modern transform domain analysis in this context stems from the absence of an appropriate transfer function model for the hybrid time discrete and continuous closed loop system this difficulty is overcome through the introduction of an equivalent difference equation model for the continuous time system with distributed inputs and outputs equivalence being in the sense that the continuous and discrete time inputs and outputs are essentially identical using the interplay between the discrete and the continuous time models solutions of the well known purely continuous time and purely discrete time standard problems extend to solutions of the problem at hand they comprise riccati equation characterizations of feasible combinations of sampling rates and bounds on the closed loop induced input output norm and parameterization of compensators we consid