analysis and design of fuzzy control system abstract a continuous time fuzzy control system which is composed of a fuzzy model and a fuzzy controller is proposed under certain conditions the proposed fuzzy control system can be regarded as a fuzzy pid control system the stability analysis of the fuzzy control system is given a sufficient condition to guarantee the stability of the proposed fuzzy control system is proposed in terms of lyapunov s method the results can be applied to the design of a fuzzy pid control system the design procedure can also be applied to the controller design with a non fuzzy model examples are given to illustrate the design of the proposed fuzzy control system

delay dependent robust h control for t s fuzzy system with interval time varying delay this paper is concerned with the problem of robust h control for uncertain t s fuzzy systems with interval time varying delay that is the delay is assumed to be a time varying function belonging to an interval by defining new lyapunov functions and making use of novel techniques to achieve delay dependence new conditions for the existence of robust h controller are obtained based on the parallel distributed compensation pdc method in this article all the conditions are shown in terms of linear matrix inequalities lmis which can be solved efficiently by using the lmi optimization techniques two numerical examples are given to illustrate the less conservatism of the proposed method

fuzzy stability criterion of a class of nonlinear systems abstract a fuzzy stability criterion of a class of nonlinear systems is discussed in accordance with the definition of stability in the sense of lyapunov first a sufficient condition that guarantees stability of a fuzzy system is given in terms of lyapunov s direct method two concepts for stability of fuzzy systems are defined locally stable and globally table second a construction procedure for lyapunov functions is presented finally the construction procedure is applied to the fuzzy stability criterion of a class of nonlinear systems that can be approximated by fuzzy systems

approaches to t s fuzzy affine model based reliable output feedback control for nonlinear ito stochastic systems this paper deals with the problem of reliable and robust mathscr h infty static output feedback sof controller synthesis for continuous time nonlinear stochastic systems with actuator faults the nonlinear stochastic plant is expressed by an ito type takagi sugeno fuzzy affine model with parametric uncertainties and a markov process is employed to model the occurrence of actuator fault the purpose is to design an admissible piecewise sof controller such that the resulting closed loop system is stochastically stable with a prescribed disturbance attenuation level in an mathscr h infty sense specifically based on a markovian lyapunov function combined with ito differential formula s procedure and some matrix inequality convexification procedures two new approaches to the reliable sof controller analysis and synthesis are proposed for the underlying stochastic fuzzy affine systems it is shown that the existence of desired reliable controllers is fully characterized in terms of strict linear matrix inequalities finally simulation examples are presented to illustrate the effectiveness and advantages of the developed methods

design of robust controllers for time delay systems the problem of stabilizing linear dynamical time delay systems subject to bounded uncertainties is investigated two memoryless feedback controllers are considered it is established that when the matching conditions are met and certain bounding relations are satisfied then the linear controller renders the zero response of the system asymptotically stable saturation type controllers are shown to guarantee that all system responses are uniformly ultimately bounded

locating p poly optimally in the extended low hierarchy the low hierarchy in np and the extended low hierarchy have turned out to be very useful in classifying many interesting language classes and almost all of them could be located optimally therein however until now the exact location of p poly remained open

the geometry of tensor calculus i this paper defines and proves the correctness of the appropriate string diagrams for various kinds of monoidal categories with duals mathematics subject classifications 1991 18d10 52b11 53a45 57m25 68q10 82b23

new robust stability conditions and design of robust stabilizing controllers for takagi sugeno fuzzy time delay systems in this paper we consider robust stability and stabilization of uncertain takagi sugeno fuzzy time delay systems where uncertainties come into the state and input matrices some stability conditions and robust stability conditions for fuzzy time delay systems have already been obtained in the literature however those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems this is true in case of designing stabilizing controllers for fuzzy time delay systems and it thus leads to a conservative fuzzy controller design as well we first consider rather relaxed robust stability conditions of uncertain fuzzy systems to this end we introduce an auxiliary system to the original fuzzy time delay system to obtain generalized delay dependent stability conditions such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay dependent stability conditions conditions we obtain here are delay dependent conditions that depend on the upper bound of time delay and are given in terms of linear matrix inequalities lmis then we compare our delay dependent stability conditions with other conditions in the literature and show that our conditions guarantee the stability of a wider class of systems than others next we consider the robust stabilization problem with memoryless and delayed state feedback controllers based on our generalized robust stability conditions we obtain delay dependent sufficient conditions for the closed loop system to be robustly stable and give a design method of robustly stabilizing controllers finally we give three examples that illustrate our results

bounded queries approximations and the boolean hierarchy this paper investigates nondeterministic bounded query classes in relation to the complexity of np hard approximation problems and the boolean hierarchy nondeterministic bounded query classes turn out be rather suitable for describing the complexity of np hard approximation problems the results in this paper take advantage of this machine based model to prove that in many cases np approximation problems have the upward collapse property that is a reduction between np approximation problems of apparently different complexity at a lower level results in a similar reduction at a higher level for example if maxclique reduces to log n approximating maxclique using many one reductions then the traveling salesman problem tsp is equivalent to maxclique under many one reductions several upward collapse theorems are presented in this paper the proofs of these theorems rely heavily on the machinery provided by the nondeterministic bounded query classes in fact these results depend on a surprising connection between the boolean hierarchy and nondeterministic bounded query classes

complexity restricted advice functions the authors consider uniform subclasses of the nonuniform complexity classes defined by karp and lipton l enseign math 28 1982 via the notion of advice functions these subclasses are obtained by restricting the complexity of computing correct advice also the effect of allowing advice functions of limited complexity to depend on the input rather than on the input s length is investigated among other results using the notions described above new characterizations of a np np cap sparse b np with a restricted access to an np oracle and c the odd levels of the boolean hierarchy are given as a consequence it is shown that every set that is nondeterministically truth table reducible to sat in the sense of rich j comput system sci 38 1989 pp 511 523 is already deterministically truth table reducible to sat furthermore it turns out that the np reduction classes of bounded versions of this reducibility coincide with the odd levels of the boolean hierarchy

an algebraic approach to h output feedback control problems abstract we derive an output feedback controller which stabilizes a system and satisfies a prescribed h norm bound of the closed loop transfer function the proposed design method is available for any system i e there are no restrictions on d12 and d21 this approach utilizes only algebraic operations thus proofs are simple and clear

output feedback robust h sup spl infin control of uncertain fuzzy dynamic systems with time varying delay this paper presents an output feedback robust h sup spl infin control problem for a class of uncertain fuzzy dynamic systems with time varying delayed state the takagi sugeno fuzzy model is employed to represent an uncertain nonlinear systems with time varying delayed state using a single quadratic lyapunov function the globally exponential stability and disturbance attenuation of the closed loop fuzzy control system are discussed sufficient conditions for the existence of robust h sup spl infin controllers are given in terms of matrix inequalities constructive algorithm for design of robust h sup spl infin controller is also developed the resulting controller is nonlinear and automatically tuned based on fuzzy operation

quadratic stabilization of continuous time systems with state delay and norm bounded time varying uncertainties this paper develops a method for designing a feedback control law to stabilize a class of uncertain linear systems the class of systems under consideration is described by a continuous time model with variable state delay and depends on time varying unknown but bounded uncertain parameters it is shown that the construction of the stabilizing controller involves solving a certain algebraic riccati equation several previous results are derived as interesting special cases finally a simulation example is presented to illustrate the analytical developments

robust h control of multiple time delay uncertain nonlinear system using fuzzy model and adaptive neural network in this paper a robust control method which combines fuzzy model based control with adaptive neural network control is presented for a class of uncertain nonlinear system with multiple time delay the fuzzy t s model with multiple time delay is adopted for the approximate modeling of the nonlinear system with some unknown uncertainties and fuzzy model based h control law is designed by means of lmi method a full adaptive rbf neural network is added to the fuzzy h control in order to guarantee the robust stability of the controlled system the effect of the unknown uncertainties and the error caused by fuzzy modeling can be overcome by adaptive tuning of the weights centers and widths of the rbf neural network on line and no constraint or matching conditions are required the stability of the designed closed loop system is thus proved the proposed method is applied to a multiple time delay nonlinear chaotic system and the simulation results show that the proposed method cannot only stabilize the chaos systems but has strong robustness against uncertainties and external disturbance

delay range dependent robust stabilization for uncertain t s fuzzy control systems with interval time varying delays this paper is concerned with robust stabilization for a class of t s fuzzy control systems with interval time varying delays an approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities the main points of the approach are i two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria ii an appropriate lyapunov krasovskii functional is constructed by including both the lower and upper bounds of the interval time varying delays and iii neither model transformation nor free weighting matrices are employed in the theoretical result derivation as a result some improved sufficient stability criteria are derived and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem numerical examples are given to demonstrate the effectiveness of the proposed approach

memoryless stabilization of uncertain dynamic delay systems riccati equation approach the authors present a procedure for obtaining the memoryless linear state feedback control of uncertain dynamic delay systems the uncertainties are time varying and within a given compact set this method is an extension of the riccati equation approach proposed by i r petersen and c v hollot 1986 the extension is straightforward also the uncertainties do not need to satisfy the matching conditions

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

switched fuzzy output feedback control and its application to a mass spring damping system this paper investigates the dynamic output feedback control problem for interval type 2 it2 fuzzy systems a switched output feedback controller which depends on the values of membership functions is constructed the membership functions of it2 fuzzy systems contain parameter uncertainties and are different from the type 1 takagi sugeno fuzzy systems based on the it2 fuzzy set theory the parameter uncertainties can be effectively obtained by upper and lower membership functions a novel it2 switched output feedback controller is designed to ensure that the closed loop system is asymptotically stable with an h infty performance finally a mass spring damping system is proposed to show the feasibility and the merit of the proposed scheme over the other existing ones

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

delay dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay this paper focuses on the delay dependent stability analysis and stabilization for fuzzy control systems with time delay based on linear matrix inequality lmi approach a delay dependent stability criteria has been developed the design schemes of stabilization via state feedback is developed and then the result is extended to the case of observer based output feedback all the researching results are presented by means of lmis two illustrative examples are given to illustrate the validity of the proposed design procedures

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

robust control for parameter uncertain delay systems in state and control input in this note we present a robust control design method for parameter uncertain systems that have delay in both state and control input through a certain algebraic riccati inequality approach a state feedback controller is obtained the controller guarantees a stability for parameter uncertainties and delays

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

robustness design of nonlinear dynamic systems via fuzzy linear control this study introduces a fuzzy linear control design method for nonlinear systems with optimal h sup spl infin robustness performance first the takagi and sugeno fuzzy linear model 1985 is employed to approximate a nonlinear system next based on the fuzzy linear model a fuzzy controller is developed to stabilize the nonlinear system and at the same time the effect of external disturbance on control performance is attenuated to a minimum level thus based on the fuzzy linear model h sup spl infin performance design can be achieved in nonlinear control systems in the proposed fuzzy linear control method the fuzzy linear model provides rough control to approximate the nonlinear control system while the h sup spl infin scheme provides precise control to achieve the optimal robustness performance linear matrix inequality lmi techniques are employed to solve this robust fuzzy control problem in the case that state variables are unavailable a fuzzy observer based h sup spl infin control is also proposed to achieve a robust optimization design for nonlinear systems a simulation example is given to illustrate the performance of the proposed design method

new approach on robust delay dependent h _ infty control for uncertain t s fuzzy systems with interval time varying delay this paper investigates the robust h infin control for takagi sugeno t s fuzzy systems with interval time varying delay by employing a new and tighter integral inequality and constructing an appropriate type of lyapunov functional delay dependent stability criteria are derived for the control problem because neither any model transformation nor free weighting matrices are employed in our theoretical derivation the developed stability criteria significantly improve and simplify the existing stability conditions also the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem numerical examples are given to demonstrate the effectiveness of the proposed methods

further remarks on additional dynamics in various model transformations of linear delay systems this paper focuses on the analysis of conservatism introduced due to some model transformations used in the control literature this work is an extension of a previous paper by the authors 1999 on additional dynamics the additional dynamics of the second order and parametrized model transformations are examined the neutral model transformation introduces additional constraints for stability which can be analyzed in a very similar manner to additional dynamics

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

delay dependent robust stability and stabilization of uncertain linear delay systems a linear matrix inequality approach this paper considers the problems of robust stability analysis and robust control design for a class of uncertain linear systems with a constant time delay the uncertainty is assumed to be norm bounded and appears in all the matrices of the state space model we develop methods for robust stability analysis and robust stabilization the proposed methods are dependent on the size of the delay and are given in terms of linear matrix inequalities

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

improved approach to robust cal h _ infty stabilization of discrete time t s fuzzy systems with time varying delays this study is concerned with the robust stabilization problem for a class of discrete time takagi sugeno t s fuzzy systems with time varying delays to improve the conditions for the solvability of the stabilization problem a nonquadratic lyapunov krasovskii functional with a triple summation term is established and a nonparallel distributed compensation non pdc scheme is adopted along with the matrixtransformation technique in addition an appropriate free weightingmatrix method is proposed to exploit novel slack variables for null sum terms especially resulting from i xi 1 xi t xi 1 xi

sampled data robust h control for t s fuzzy systems with time delay and uncertainties abstract this paper investigates sampled data robust h control for t s fuzzy systems with time delay and uncertainties by introducing the free weighting matrices to deal with the integral items and converting the coupling time varying matrix inequalities into a group of decoupling matrix inequalities an innovative delay dependent stabilization criterion is first presented then a sampled data h controller is designed to stabilize the t s fuzzy system to achieve the prescribed disturbance attenuation level which is dependent on both the size of state delay and upper bound of allowable sampling period since 1 the sawtooth structure of delay is fully considered 2 neither model transformation nor bounding techniques are employed in deriving the delay dependent results and 3 none of the integral items are arbitrarily ignored and magnified the less conservative results can be expected a practical application example is given to demonstrate the effectiveness of the proposed methods

robust fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances a novel decoupled approach unlike the l 2 gain h control case the l gain control problem is dealing with persistent bounded disturbances this study introduces l gain fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables do not depend on the state variables estimated by a fuzzy observer a novel decoupled method is proposed in this study to transform the non lmi conditions into some lmi forms by the proposed decoupled method and the genetic algorithm the l gain fuzzy observer based fuzzy control problem can be easily solved by an lmi based method

memoryless stabilization of uncertain linear systems including time varying state delays the problem of stabilizing a class of uncertain time delay systems via memoryless linear feedback is examined the systems under consideration are linear systems with time varying state delays they also contain uncertain parameters possibly time varying whose values are known only to within a prescribed compact bounding set the main contribution given is to enlarge the class of time delay systems for which one can construct a stabilizing memoryless linear feedback controller within this framework a novel notion of robust memoryless stabilizability is first introduced via the method of lyapunov functionals then a sufficient condition for the stabilizability is proposed it is shown that solvability of a parameterized riccati equation can be used to determine whether the time delay system satisfies the sufficient condition if there exists a positive definite symmetric solution satisfying the riccati equation a suitable memoryless linear feedback law can be derived

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

analysis and synthesis of nonlinear time delay systems via fuzzy control approach takagi sugeno ts fuzzy models 1985 1992 can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output i o submodels in this paper the ts fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete time nonlinear systems with time delay the ts fuzzy models with time delay are presented and the stability conditions are derived using lyapunov krasovskii approach we also present a stabilization approach for nonlinear time delay systems through fuzzy state feedback and fuzzy observer based controller sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities an illustrative example based on the cstr model is given to design a fuzzy controller

double construction for crossed hopf coalgebras abstract we provide an analog of the drinfeld quantum double construction in the context of crossed hopf group coalgebras introduced by turaev we prove that provided the base group is finite the double of a semisimple crossed hopf group coalgebra is both modular and unimodular

delay dependent robust h sub spl infin control for t s fuzzy systems with time delay this paper focuses on the problem of delay dependent robust fuzzy control for a class of nonlinear delay systems via state feedback the takagi sugeno t s fuzzy model is adopted for representing a nonlinear system with time delayed state a delay dependent stabilization criterion is first presented then the methods of robust stabilization and robust h sub spl infin control are developed which are dependent on the size of the delay and are based on the solutions of linear matrix inequalities lmis finally a design example of robust h sub spl infin controller for uncertain nonlinear systems is given to illustrate the effectiveness of the approaches proposed in this paper

quantum koszul complexes for majid s braided lie algebras a yang baxter operator was canonically associated to any cocommutative braided lie algebra as defined by majid applying previous results we construct quantum koszul complexes for braided lie algebras with respect to this operator in the usual case the complexes reduce to the chevalley eilenberg complexes for classical lie algebras

robust controllability of t s fuzzy model based control systems with parametric uncertainties the robust controllability problem for the takagi sugeno t s fuzzy model based control systems is studied in this paper under the assumption that the nominal t s fuzzy model based control systems are locally controllable i e each fuzzy rule of the nominal t s fuzzy model based control systems has a full row rank for its controllability matrix a sufficient condition is proposed to preserve the assumed property when the parameter uncertainties are added into the nominal t s fuzzy model based control systems the proposed sufficient condition can provide the explicit relationship of the bounds on parameter uncertainties to preserve the assumed property besides a robustly global controllability condition and the related robustly global stabilizability condition of the uncertain t s fuzzy model based control systems are also presented in this paper a nonlinear mass spring damper mechanical system with parameter uncertainties is given as an example to illustrate the application of the proposed sufficient conditions

h spl infin output feedback controller design for linear systems with time varying delayed state this paper considers the h spl infin controller design problem for linear systems with time varying delays in states the authors obtain sufficient conditions for the existence of h spl infin controllers in terms of three linear matrix inequalities lmis these sufficient conditions are dependent on the maximum value of the time derivative of time varying delay furthermore they briefly explain how to construct such controllers from the positive definite solutions of their lmis and give an example

memoryless h controller design for linear systems with delayed state and control we present a memoryless h control design method for linear time invariant systems that have no parametric uncertainty but delay in the state and control based on the riccati equation approach we design a memoryless linear time invariant state feedback control law which guarantees the asymptotic stability of the closed loop control system and reduces the effect of the disturbance input on the controlled output to a prescribed level

delay dependent stability and h control for a class of fuzzy descriptor systems with time delay this paper addresses issues of stability analysis and h control for a class of fuzzy time delay descriptor systems described by an extended takagi sugeno t s fuzzy model a delay dependent stability criterion is first presented and a h control synthesis approach is then developed both the stability criterion and the h controller synthesis are based on the solutions of linear matrix inequalities lmis finally two examples are given to illustrate the effectiveness of the approaches proposed in this paper

robust h control of takagi sugeno fuzzy systems with state and input time delays this paper addresses the robust h fuzzy control problem for nonlinear uncertain systems with state and input time delays through takagi sugeno t s fuzzy model approach the delays are assumed to be interval time varying delays and no restriction is imposed on the derivative of time delay based on lyapunov krasoviskii functional method delay dependent sufficient conditions for the existence of an h controller are proposed in linear matrix inequality lmi format illustrative examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology

a new design of delay dependent robust cal h _ bm infty filtering for discrete time t s fuzzy systems with time varying delay this paper investigates the problem of delay dependent robust h infin filtering design for a class of uncertain discrete time state delayed takagi sugeno t s fuzzy systems the state delay is assumed to be time varying and of an interval like type which means that both the lower and upper bounds of the time varying delay are available the parameter uncertainties are assumed to have a structured linear fractional form based on a novel fuzzy basis dependent lyapunov krasovskii functional combined with finsler s lemma and an improved free weighting matrix technique for delay dependent criteria a new sufficient condition for robust h infin performance analysis is first derived and then the filter synthesis is developed it is shown that by using a simple linearization technique incorporating a bounding inequality a unified framework can be developed such that both the full order and reduced order filters can be obtained by solving a set of linear matrix inequalities lmis which are numerically efficient with commercially available software finally simulation examples are provided to illustrate the advantages and less conservatism of the proposed approach

reliable h_ infty control for discrete time fuzzy systems with infinite distributed delay in this paper the problem of reliable h control is investigated for discrete time takagi sugeno t s fuzzy systems with infinite distributed delay and actuator faults a discrete time homogeneous markov chain is used to represent the stochastic behavior of actuator faults in terms of a stochastic fuzzy lyapunov functional a sufficient condition is proposed to ensure that the resultant closed loop system is exponentially stable in the mean square sense with an h performance index based on the derived condition the reliable h control problem is solved and an explicit expression of the desired controller is also given the case of no failure in the actuator is also considered a numerical example is given to demonstrate that our results are effective and less conservative

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

on relaxed lmi based designs for fuzzy regulators and fuzzy observers relaxed conditions for stability of nonlinear continuous and discrete time systems given by fuzzy models are presented a theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature numerical results exemplify this fact these results are also used for fuzzy regulators and observers designs the nonlinear systems are represented by fuzzy models proposed by takagi and sugeno 1985 the stability analysis and the design of controllers are described by linear matrix inequalities that can be solved efficiently using convex programming techniques the specification of the decay rate constrains on control input and output are also discussed

restricted information from nonadaptive queries to np we investigate classes of sets that can be decided by bounded truth table reductions to an np set in which evaluators donothave full access to the answers to the queries but get only restricted information such as the number of queries that are in the oracle set or even just this number modulom for somem 2 we also investigate the case in which evaluators are nondeterministic we show that when we vary the information that the evaluators get this can change the resulting power of the evaluators we locate all these classes within levels of the boolean hierarchy which allows us to compare the complexity of such classes