describing function method for stability analysis of pd and pi fuzzy controllers a fuzzy logic controller saturates outside the universe of discourse region this saturation gives rise to a universal nonlinearity for this type of controller in this paper the effects of this nonlinearity are analyzed for the most usual fuzzy controllers pd and pi fuzzy controllers it is shown that due to this saturation some pathological behaviors such as oscillations or unstable limit cycles can occur the methodology employed in the analysis is based on the describing function which is determined for pd and pi fuzzy controllers one example illustrates the relevance of the proposed methodology

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

analysis of the fuzzy controllability property and stabilization for a class of t s fuzzy models in this paper the controllability property for a class of takagi sugeno t s fuzzy models is analyzed while a fully nonlinear stabilizer is designed in a practical way it is shown that global fuzzy stabilizers can be constructed in a nonconservative way by means of a relatively simple approach the existence of such controllers depends on the fuzzy controllability conditions which are derived in a straightforward way the main advantage of the proposed approach is that the convergence of the closed loop system can be imposed arbitrarily some examples are given in order to illustrate the validity of the method finally the proposed controller is applied on an underactuated system known as pendubot and the results are compared with an stabilizer designed on the basis of lmis

the stability of two station multitype fluid networks this paper studies the fluid models of two station multiclass queueing networks with deterministic routing a fluid model is globally stable if the fluid network eventually empties under each nonidling dispatch policy we explicitly characterize the global stability region in terms of the arrival and service rates we show that the global stability region is defined by the nominal workload conditions and the virtual workload conditions and we introduce two intuitively appealing phenomena virtual stations and push starts that explain the virtual workload conditions when any of the workload conditions is violated we construct a fluid solution that cycles to infinity showing that the fluid network is unstable when all the workload conditions are satisfied we solve a network flow problem to find the coefficients of a piecewise linear lyapunov function the lyapunov function decreases to zero proving that the fluid level eventually reaches zero under any nonidling dispatch policy under certain assumptions on the inter arrival and service time distributions a queueing network is stable or positive harris recurrent if the corresponding fluid network is stable thus the workload conditions are sufficient to ensure the global stability of two station multiclass queueing networks with deterministic routing

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

heavy traffic optimality of a stochastic network under utility maximizing resource allocation we study a stochastic network that consists of a set of servers processing multiple classes of jobs each class of jobs requires a concurrent occupancy of several servers while being processed and each server is shared among the job classes in a head of the line processor sharing mechanism the allocation of the service capacities is a real time control mechanism in each network state the resource allocation is the solution to an optimization problem that maximizes a general utility function whereas this resource allocation optimizes in a greedy fashion with respect to each state we establish its asymptotic optimality in terms of a deriving the fluid and diffusion limits of the network under this allocation scheme and b identifying a cost function that is minimized in the diffusion limit along with a characterization of the so called fixed point state of the network

stabilization of networked stochastic time delay fuzzy systems with data dropout this paper deals with the problem of stabilization for networked stochastic systems with transmitted data dropout the plant in the networked control system ncs under consideration is a discrete stochastic time delay nonlinear system represented by a takagi sugeno fuzzy model exponential stability criteria of the ncs are developed by using a common quadratic lyapunov function and a fuzzy lyapunov function respectively a stabilization controller with convergence rate constraint can be designed by solving a set of linear matrix inequalities that is numerically feasible with commercially available software three numerical examples are presented to demonstrate the effectiveness of the proposed methods

robust h sub spl infin disturbance attenuation for a class of uncertain discrete time fuzzy systems the paper is concerned with robust stabilization and h sub spl infin control of a class of uncertain discrete time fuzzy systems the class of uncertain systems is described by state space takagi sugeno ts fuzzy models with linear nominal parts and norm bounded parameter uncertainties in the state and output equations first a sufficient condition on robust stability of the fuzzy models is proposed then h sub spl infin disturbance attenuation performance of the fuzzy models is analyzed some sufficient conditions are derived on robust h sub spl infin disturbance attenuation in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties a numerical example shows the use of the results on the stabilization and h sub spl infin disturbance attenuation of a class of discrete time nonlinear systems via fuzzy switch

h sub spl infin state feedback controller design for discrete time fuzzy systems using fuzzy weighting dependent lyapunov functions for discrete time takagi sugeno ts fuzzy systems we propose an h sub spl infin state feedback fuzzy controller associated with a fuzzy weighting dependent lyapunov function the controller which is designed via parameterized linear matrix inequalities plmis employs not only the current time but also the one step past information on the time varying fuzzy weighting functions appropriately selecting the structures of variables in the plmis allows us to find an lmi formulation as a special case

quadratic stability analysis of fuzzy model based control systems using staircase membership functions this paper presents the stability analysis of fuzzy model based fmb control systems staircase membership functions are introduced to facilitate the stability analysis through the staircase membership functions approximating those of the fuzzy model and fuzzy controller the information of the membership functions can be brought into the stability analysis based on the lyapunov stability theory stability conditions in terms of linear matrix inequalities lmis are derived in a simple and easy to understand manner to guarantee the system stability the proposed stability analysis approach offers a nice property that includes the membership functions of both fuzzy model and fuzzy controller in the lmi based stability conditions for a dedicated fmb control system furthermore the proposed stability analysis approach can be applied to the fmb control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same greater design flexibility is allowed to choose the membership functions during the design of fuzzy controllers by employing membership functions with simple structure it is possible to lower the structural complexity and the implementation cost simulation examples are given to illustrate the merits of the proposed approach

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

diffusion limit of fair resource control stationarity and interchange of limits we study a resource sharing network where each job requires the concurrent occupancy of a subset of links servers resources and each link s capacity is shared among job classes that require its service the real time allocation of the service capacity among job classes is determined by the so called proportional fair scheme which allocates the capacity among job classes taking into account the queue lengths and the shadow prices of link capacity we show that the usual traffic condition is necessary and sufficient for the diffusion limit to have a stationary distribution we also establish the uniform stability of the prelimit networks and hence the existence of their stationary distributions to justify the interchange of two limits the limit in time and limit in diffusion scaling we identify a bounded workload condition and show it is a sufficient condition to justify the interchange for the stationary distributions and their moments this last result is essential for the validity of the diffu

fault detection for fuzzy systems with intermittent measurements this paper investigates the problem of fault detection for takagi sugeno t s fuzzy systems with intermittent measurements the communication links between the plant and the fault detection filter are assumed to be imperfect i e data packet dropouts occur intermittently which appear typically in a network environment and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the unreliable communication links the aim is to design a fuzzy fault detection filter such that for all data missing conditions the residual system is stochastically stable and preserves a guaranteed performance the problem is solved through a basis dependent lyapunov function method which is less conservative than the quadratic approach the results are also extended to t s fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities which can be readily solved via standard numerical software two examples are provided to illustrate the usefulness and applicability of the developed theoretical results

limit theorems for markovian bandwidth sharing networks with rate constraints bandwidth sharing networks provide a natural modeling framework for describing the dynamic flow level interaction among elastic data transfers in computer and communication systems and can be used to develop traffic pricing charging mechanisms at the same time such models are exciting from an operations research perspective because their analysis requires techniques from stochastic modeling and optimization in this paper we develop a framework to approximate bandwidth sharing networks under the assumption that the number of users as well as the capacities of the system are large and the assumption that the traffic that each user is allowed to submit is bounded above by some rate which is standard in practice we also assume that customers on each route in the network abandon according to exponential patience times under markovian assumptions we develop fluid and diffusion approximations which are quite tractable for most parameter combinations the invariant distribution is multivariate normal with mean and diffusion coefficients that can be computed in polynomial time as a function of the size of the network

stationary distribution convergence for generalized jackson networks in heavy traffic in a recent paper gamarnik and zeevi gamarnik d a zeevi 2006 validity of heavy traffic steady state approximations in open queueing networks ann appl probab 16 1 56 90 it was shown that under suitable conditions stationary distributions of the scaled queue lengths process for a generalized jackson network converge to the stationary distribution of the associated reflected brownian motion in the heavy traffic limit the proof relied on certain exponential integrability assumptions on the primitives of the network in this note we show that the above result holds under much weaker integrability conditions we provide an alternative proof of this result assuming in addition to natural heavy traffic and stability assumptions only standard independence and square integrability conditions on the network primitives that are commonly used in heavy traffic analysis furthermore under additional integrability conditions we establish convergence of moments of stationary distributions

stability analysis of polynomial fuzzy model based control systems using switching polynomial lyapunov function this paper investigates the stability problem of polynomial fuzzy model based control system which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop a switching polynomial lyapunov function consisting of a number of local polynomial lyapunov functions is proposed to investigate the system stability it demonstrates a nice property in favor of the stability analysis that each local polynomial lyapunov function transits continuously to each other as different local polynomial lyapunov functions are employed to investigate the system stability according to the operating domain relaxed stability conditions compared with the stability analysis result with a common lyapunov function can be developed in order to allow a greater design flexibility for the polynomial fuzzy controller the proposed polynomial fuzzy model based control scheme does not require that both the polynomial fuzzy model and polynomial fuzzy controller share the same premise membership functions stability conditions in terms of sum of squares are obtained to guarantee system stability and facilitate control synthesis simulation examples are given to verify the stability analysis results and demonstrate the effectiveness of the proposed polynomial fuzzy control scheme

asymptotic stationarity of queues in series and the heavy traffic approximation one deals with a system of queues in series that is to say a number of queues through which a unit passes in turn spending a waiting time including service in any particular one and proceeding to the next succeeding queue immediately the service time is completed the first main result deals with the asymptotic behaviour of the vector of waiting times of a unit in each queue and of the time which a unit spends in the tandem queue the second main result deals with the heavy traffic approximation of the mentioned characteristics

validity of heavy traffic steady state approximations in multiclass queueing networks the case of queue ratio disciplines a class of stochastic processes known as semi martingale reflecting brownian motions srbms is often used to approximate the dynamics of heavily loaded queueing networks in two influential papers bramson bramson m 1998 state space collapse with applications to heavy traffic limits for multiclass queueing networks queueing systems 30 89 148 and williams williams rj 1998b diffusion approximations for open multiclass queueuing networks sufficient conditions involving state space collapse queueing systems 30 27 88 laid out a general and structured approach for proving the validity of such heavy traffic approximations in which an srbm is obtained as a diffusion limit from a sequence of suitably normalized workload processes however for multiclass networks it is still not known in general whether the steady state distribution of the srbm provides a valid approximation for the steady state distribution of the original network in this paper we study the case of queue ratio disciplines and provide a set of sufficient conditions under which the above question can be answered in the affirmative in addition to standard assumptions made in the literature towards the stability of the pre and post limit processes and the existence of diffusion limits we add a requirement that solutions to the fluid model are attracted to the invariant manifold at a linear rate for the special case of static priority networks such linear attraction is known to hold under certain conditions on the network primitives the analysis elucidates interesting connections between stability of the pre and post limit processes their respective fluid models and state space collapse and identifies the respective roles played by all of the above in establishing validity of heavy traffic steady state approximations

heavy traffic limits for queues with many exponential servers two different kinds of heavy traffic limit theorems have been proved for s server queues the first kind involves a sequence of queueing systems having a fixed number of servers with an associated sequence of traffic intensities that converges to the critical value of one from below the second kind which is often not thought of as heavy traffic involves a sequence of queueing systems in which the associated sequences of arrival rates and numbers of servers go to infinity while the service time distributions and the traffic intensities remain fixed with the traffic intensities being less than the critical value of one in each case the sequence of random variables depicting the steady state number of customers waiting or being served diverges to infinity but converges to a nondegenerate limit after appropriate normalization however in an important respect neither procedure adequately represents a typical queueing system in practice because in the heavy traffic limit an arriving customer is either a

typical takagi sugeno pi and pd fuzzy controllers analytical structures and stability analysis in the first part of this paper we investigate explicit structure of the typical takagi sugeno ts fuzzy pi and pd controllers by typical we mean the use of at least three trapezoidal or triangular input fuzzy sets for each input variable fuzzy rules with linear consequent zadeh fuzzy logic and operator and the centroid defuzzifier this configuration covers many ts fuzzy controllers in the literature we mathematically prove these fuzzy controllers to be nonlinear pi or pd controllers with proportional gain and integral gain or derivative gain changing with output of the controlled system we reveal these fuzzy controllers to be inherently nonlinear gain scheduling pi or pd controllers with different variable gains in different regions of input space the gains constantly change even in the same region and switch continuously and smoothly between adjacent regions the explicit structural expressions of the fuzzy controllers are derived and their characteristics including the bounds and geometrical shape of the gain variation are studied in the second part of the paper we apply the small gain theorem to the derived structures of the fuzzy controllers and establish a sufficient global bibo stability criterion for nonlinear systems controlled by the fuzzy controllers local stability is also examined

stability analysis of piecewise discrete time linear systems presents a stability analysis method for piecewise discrete time linear systems based on a piecewise smooth lyapunov function it is shown that the stability of the system can be established if a piecewise lyapunov function can be constructed and moreover the function can be obtained by solving a set of linear matrix inequalities lmis that is numerically feasible with commercially available software

h filtering of discrete time fuzzy systems via basis dependent lyapunov function approach this paper is concerned with the h filtering problem for a class of discrete time fuzzy systems attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the h sense by using basis dependent lyapunov functions sufficient conditions for the solvability of this problem are obtained it has been shown that the h filtering problem can be solved as a linear matrix inequality lmi optimization problem two examples are provided to demonstrate the applicability of the proposed approach

fluid limits for bandwidth sharing networks with rate constraints bandwidth sharing networks as introduced by roberts and massoulie roberts jw massoulie l 1998 bandwidth sharing and admission control for elastic traffic proc itc specialist seminar yokohama japan massoulie and roberts massoulie l roberts jw 1999 bandwidth sharing objectives and algorithms proc ieee infocom books in statistics new york 1395 1403 model the dynamic interaction among an evolving population of elastic flows competing for several links with policies based on optimization procedures such models are of interest both from a queueing theory and operations research perspective in the present paper we focus on bandwidth sharing networks with capacities and arrival rates of a large order of magnitude compared to transfer rates of individual flows this regime is standard in practice in particular we extend previous work by reed and zwart reed j zwart b 2010 limit theorems for bandwidth sharing networks with rate constraints revised preprint http people stern nyu e

delay dependent stabilization for stochastic fuzzy systems with time delays this paper is concerned with the delay dependent stabilization problem for a class of time delay stochastic fuzzy systems the time delays are assumed to appear in both the state and the control input the purpose is the design of a state feedback fuzzy controller such that the resulting closed loop system is asymptotically stable in the mean square a delay dependent condition for the solvability of this problem is obtained in terms of relaxed linear matrix inequalities lmis by solving these lmis a desired controller can be obtained finally a numerical example is given to demonstrate the effectiveness of the present results

behavior of solutions near manifolds of periodic solutions abstract consider an autonomous differential system x f x of dimension n that admits a k dimensional invariant manifold in x space represented by a k parameter family of periodic solutions then k characteristic multipliers of the corresponding variational equation are equal to 1 under the hypothesis that none of the remaining n k characteristic multipliers has modulus 1 the behavior of the solutions of x f x near is investigated the main results are the description of a neighborhood of in terms of stable and unstable manifolds and the statement that whenever a solution of x f x approaches the invariant manifold as t it tends to with asymptotic amplitude and phase

new results on delay dependent robust stability criteria of uncertain fuzzy systems with state and input delays this paper focuses on the delay dependent stability analysis and stabilization for uncertain t s fuzzy control systems with state and input delays the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology in fact these techniques lead to more general and less conservative stability conditions that guarantee a wide stability region our delay dependent stability conditions thus obtained are given in terms of linear matrix inequalities lmis finally some examples are included to show that the proposed criteria improve the existing results significantly

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

cal h _ infty state feedback control design for fuzzy systems using lyapunov functions with quadratic dependence on fuzzy weighting functions this paper proposes a method for designing an hinfin state feedback fuzzy controller for discrete time takagi sugeno t s fuzzy systems to derive less conservative hinfin stabilization conditions this paper enhances the interactions among the fuzzy subsystems using a multiple lyapunov function with quadratic dependence on fuzzy weighting functions besides for more allocation of the nonlinearity to the fuzzy control system this paper introduces a slack variable that is quadratically dependent on the one step past fuzzy weighting functions as well as the current ones in the derivation the hinfin stabilization conditions are formulated in terms of parameterized linear matrix inequalities plmis which are reconverted into lmi conditions with the help of an efficient relaxation technique

a new approach to robust and non fragile h control for uncertain fuzzy systems this paper investigates the robust h control and non fragile control problems for takagi sugeno t s fuzzy systems with linear fractional parametric uncertainties the robust h control problem is to design a state feedback controller such that the robust stability and a prescribed h performance of the resulting closed loop system is ensured and the non fragile h control problem is to design a state feedback controller with parameter uncertainties based on the linear matrix inequality lmi approach new sufficient conditions for the solvability of the two problems are obtained it is shown that the desired state feedback fuzzy controller can be constructed by solving a set of lmis numerical examples are also provided to demonstrate the effectiveness of the proposed design method

utility maximizing resource control diffusion limit and asymptotic optimality for a two bottleneck model we study a stochastic network that consists of two servers shared by two classes of jobs class 1 jobs require a concurrent occupancy of both servers while class 2 jobs use only one server the traffic intensity is such that both servers are bottlenecks meaning the service capacity is equal to the offered workload the real time allocation of the service capacity among the job classes takes the form of a solution to an optimization problem that maximizes a utility function we derive the diffusion limit of the network and establish its asymptotic optimality in particular we identify a cost objective associated with the utility function and show that it is minimized at the diffusion limit by the utility maximizing allocation within a broad class of fair allocation schemes the model also highlights the key issues involved in multiple bottlenecks

stability analysis of the simplest takagi sugeno fuzzy control system using circle criterion in this paper we present two sufficient conditions in the frequency domain for the global stability analysis of the simplest takagi sugeno t s fuzzy control system based on the circle criterion and its graphical interpretation these conditions are significant in graphically designing the simplest t s fuzzy controller in the frequency domain four numerical examples are provided to demonstrate the efficiency of our two frequency domain based conditions furthermore this t s fuzzy controller and the linear proportional controllers are also compared it is concluded that the simplest t s fuzzy controller can outperform the linear proportional controllers in a noisy environment with external disturbances

asymptotic phase revisited abstract we discuss the classical problem on asymptotic phase of periodic orbits of planar systems the existence of asymptotic phase for non hyperbolic periodic orbits is completely determined with hypotheses on the derivatives of a poincare map and a return time map smoothness of the vector field turns out to be crucial for existence of asymptotic phase for hyperbolic periodic orbits a new proof for the existence of invariant foliations is provided

a robust multi objective dpdc for uncertain t s fuzzy systems this paper offers a design procedure for a robust pole placement problem with h objective via dynamic output feedback control for a class of uncertain fuzzy systems takagi sugeno t s fuzzy system is used for modeling and dynamic parallel distributed compensation dpdc technique is employed in the controller design solutions to the problems are derived in terms of a family of linear matrix inequalities lmis and uncertainties are directly considered in the conditions that determine the controller effectiveness of the proposed design technique is illustrated by simulation for an inverted pendulum system

a descriptor system approach to non fragile h control for uncertain fuzzy neutral systems in this paper the problem of non fragile h control for a class of uncertain takagi sugeno t s fuzzy neutral systems with linear fractional parametric uncertainties is considered the non fragile h control problem is to design a state feedback controller with parameter uncertainties such that the l 2 induced gain of the mapping from the exogenous input to the controlled output is less than some prescribed level based on lyapunov krasovskii functional the descriptor model transformation and lmi approach new sufficient conditions for solvability of this problem are obtained it is shown that by a novel controller design method the desired state feedback fuzzy controller can be constructed by solving a set of lmis and the minimum h disturbance attenuation level can be obtained via using the lmi algorithm mincx finally an illustrative numerical example is provided to demonstrate correctness and effectiveness of the theoretical results

limit cycle prediction of a fuzzy control system based on describing function method a limit cycle is the phenomenon that can be observed in systems composed of nonlinear elements the phenomenon is of fundamental importance in nonlinear systems and as far as the design of a nonlinear system is concerned it should be considered along with the stability analysis in the paper the limit cycle of a system controlled by a fuzzy logic controller flc is addressed via some of the classical control techniques used to analyze nonlinear systems in the frequency domain first reasonable assumptions are made on the structure of the flc by using fuzzy basis functions fbfs and the describing function of the flc is derived to analyze and predict the existence of the limit cycle of the closed loop system including the flc finally computer simulation is performed to show how the analysis given in the paper is used to predict the existence of the limit cycle of the fuzzy control system

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

robust h_ infty fuzzy output feedback control with multiple probabilistic delays and multiple missing measurements in this paper the robust h control problem is investigated for a class of uncertain discrete time fuzzy systems with both multiple probabilistic delays and multiple missing measurements a sequence of random variables all of which are mutually independent but obey the bernoulli distribution is introduced to account for the probabilistic communication delays the measurement missing phenomenon occurs in a random way the missing probability for each sensor satisfies a certain probabilistic distribution in the interval here the attention is focused on the analysis and design of h fuzzy output feedback controllers such that the closed loop takagi sugeno t s fuzzy control system is exponentially stable in the mean square the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of admissible output feedback controllers which ensures the exponential stability as well as the prescribed h performance the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one that is solved by the semi definite program method simulation results are utilized to demonstrate the effectiveness of the proposed design technique in this paper

lmi based robust stability analysis for fuzzy feedback linearization regulators with its applications in order to cope with parametric uncertainties of nonlinear systems a numerical analysis method of a robust feedback linearization control scheme based on fuzzy models is proposed the fuzzy feedback linearization control scheme ensures that the control operates stably under bounded parametric uncertainties for the system with known uncertainty bounds linear matrix inequality based robust stability condition is derived and a robust fuzzy feedback linearization regulators can be designed by choosing the control parameters satisfying the inequalities which give sufficient conditions for the closed loop system to be stable to verify the validity and effectiveness of the designed stability analysis methods the suggested analysis techniques are applied to a balancing control of inverted pendulum systems

invariant manifolds with asymptotic phase this paper is concerned with invariant manifolds allowing a generic approach to solutions of the underlying autonomous differential system only this means that any solution approaching such an invariant manifold m ultimately behaves like a particular solution on j4 in the sense that the difference n t i l of the two solutions tends to 0 as t cq in other words only solutions on the stable manifold of m can approach m as f cc invariant manifolds with that property are said to have an asymptotic phase the simplest nontrivial example of an invariant manifold with asymptotic phase is the orbit of an isolated periodic solution whose floquet multipliers lie all but one in the open unit disc of the complex plane malkin 12 proved a manifold of stationary solutions to have an asymptotic phase if each of these solutions has all eigenvalues with nonpositive real parts and if in addition the number of eigenvalues on the imaginary axis equals the dimension of the manifold more generally a k dimensional manifold generated by a family of periodic solutions has an asymptotic phase if all but k floquet multipliers have modulus less than 1 see hale stokes 9 conditions for a torus to be asymptotically stable with asymptotic phase are given by samoilenko 13 and coppel 5 invariant manifolds without any specified structure are considered by fenichel 6 7 and in kirchgraber s note 111 moreover each center manifold has an asymptotic phase if the corresponding equilibrium is stable see carr al amood 4 and henry lo in any case the condition guaranteeing the existence of an asymptotic phase amounts to the fact that the decay rate of solutions toward the manifold is greater than the decay rate of the solutions within the manifold in each of the cases quoted so far the invariant manifold is asymptotically stable and thus the question arises whether an asymptotic phase can exist only in connection with asymptotic stability a negative answer to this question is given by the author in l 21 where hyperbolic manifolds of periodic solutions are proved to have an asymptotic phase in l the manifold is supposed to be compact while the noncompact case is treated in 2 under the restriction that the generating family of periodic solutions has an amplitude independent period recently hale massatt 8 extended the corresponding result for manifolds of stationary solutions to a certain class of partial differential equations in this paper we drop the periodicity assumption of the flow on the given manifold and prove the following result a compact invariant manifold has an asymptotic phase if the manifold is hyperbolic assumption hl and carries a flow parallel in the sense of our assumption h2 this includes most of the aforementioned results

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

a stochastic network under proportional fair resource control diffusion limit with multiple bottlenecks we study a multiclass stochastic processing network operating under the so called proportional fair allocation scheme and following the head of the line processor sharing discipline specifically each server s capacity is shared among the job classes that require its service and it is allocated in every state of the network among the first waiting job of each class to maximize a log utility function we establish the limiting regime of the network under diffusion scaling allowing multiple bottlenecks in the network and relaxing some of the conditions required in prior studies we also identify the class of allocation schemes among which the proportional fair allocation minimizes a quadratic cost objective function of the diffusion scaled queue lengths and we illustrate the limitation of this asymptotic optimality through a counterexample

control of rational systems using linear fractional representations and linear matrix inequalities abstract every system of the form x f x u y g x u where f and g are rational functions of the state x and linear functions of the input u possesses a linear fractional representation lfr in this lfr the system is viewed as an lti system connected with a diagonal feedback element linear in the state we devise an algorithm for computing lfrs based on this construction we give sufficient conditions for various properties to hold for the open loop system these include checking whether a given polytope is stable finding a lower bound on the decay rate of trajectories initiating in this polytope computing an upper bound on the l2 gain etc all these conditions are obtained by analyzing the properties of a differential inclusion related to the lfr and given as convex optimization problems over linear matrix inequalities lmis we show how to use this approach for static state feedback synthesis we then generalize the results to dynamic output feedback synthesis in the case when f and g are linear in every state coordinate that is not measured extensions towards a class of nonrational and uncertain nonliner systems are discussed

robust h control for discrete time fuzzy systems via basis dependent lyapunov functions this paper deals with the robust h control problem for a class of discrete time fuzzy systems with uncertainty the uncertainty is assumed to be of structured linear fractional form by using basis dependent lyapunov function an h control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov and the system matrices which makes the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis it is expected that the basis dependent results are less conservative than the basis independent ones due to the introduction of basis dependent lyapunov function finally numerical examples including the discrete chaotic lorenz system are also given to demonstrate the applicability of the proposed approach

fluid limits for processor sharing queues with impatience we investigate a processor sharing queue with renewal arrivals and generally distributed service times impatient jobs may abandon the queue or renege before completing service the random time representing a job s patience has a general distribution and may be dependent on its initial service time requirement a scaling procedure that gives rise to a fluid model with nontrivial yet tractable steady state behavior is presented this fluid model captures many essential features of the underlying stochastic model and it is used to analyze the impact of impatience in processor sharing queues

h_ infty fuzzy control of nonlinear systems under unreliable communication links this paper investigates the problem of h infin fuzzy control of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s fuzzy model and the control strategy takes the form of parallel distributed compensation the communication links existing between the plant and controller are assumed to be imperfect that is data packet dropouts occur intermittently which appear typically in a network environment and stochastic variables satisfying the bernoulli random binary distribution are utilized to model the unreliable communication links attention is focused on the design of h infin controllers such that the closed loop system is stochastically stable and preserves a guaranteed h infin performance two approaches are developed to solve this problem based on the quadratic lyapunov function and the basis dependent lyapunov function respectively several examples are provided to illustrate the usefulness and applicability of the developed theoretical results

feedback control of nonlinear systems by extended linearization for single input multiple output nonlinear systems we consider a design method based on the family of linearizations of the system parameterized by constant operating points nonlinear state feedback control laws and observer state feedback control laws are designed such that the eigenvalues of the family of linearized closed loop systems are placed at specified values that are locally invariant with respect to the closed loop operating point the method is illustrated by application to the problem of automatically balancing an inverted pendulum

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

graphical l2 stability analysis of takagi sugeno control systems in the frequency domain in this paper the upper bound of the l2 gain of the continuous time siso takagi sugeno t s fuzzy system is first graphically obtained in the frequency domain based on this upper bound of the l2 gain the l2 stability of the above t s fuzzy control system is next investigated by using the small gain theorem and circle criterion two sufficient conditions are derived which can be employed to graphically investigate the l2 stability of certain kind of t s fuzzy control system in the frequency domain one numerical example is presented to illustrate how the l2 stability of the simplified continuous time t s fuzzy system can be graphically examined

stability analysis of fuzzy control systems in this paper we present a general review of the stability issue as related to fuzzy control systems the concept of stability and the general criterion used for fuzzy control systems are discussed the intuitive and nonlinear system stability analysis of fuzzy control systems are given popov s technique is proposed to test the stability of fuzzy systems

period function and normalizers of vector fields in rn with n 1 first integrals we extend the theory that relates period function normalizers and first integrals which has been widely developed in r2 to any dimension in particular we show how to find n 1 independent normalizers of vector fields in rn with n 1 independent first integrals a formula for the derivatives of the period function is obtained and a necessary and sufficient condition for isochronicity is also proved these results generalize previous works of freire gasull and guillamon sabatini and villarini

fluid limits for bandwidth sharing networks in overload bandwidth sharing networks as considered by roberts and massoulie 28 roberts jw massoulie l 1998 bandwidth sharing and admission control for elastic traffic proc itc specialist seminar yokohama japan provide a natural modeling framework for describing the dynamic flow level interaction among elastic data transfers under mild assumptions it has been established that a wide family of so called fair bandwidth sharing strategies achieve stability in such networks provided that no individual link is overloaded in the present paper we focus on bandwidth sharing networks where the load on one or several of the links exceeds the capacity to characterize the overload behavior we examine the fluid limit which emerges when the flow dynamics are scaled in both space and time we derive a functional equation characterizing the fluid limit and show that any strictly positive solution must be unique which in particular implies the convergence of the scaled number of flows to the fluid limit for nonz

robust h filter design for uncertain fuzzy neutral systems this paper investigates the problem of robust h filtering for a class of uncertain takagi sugeno t s fuzzy neutral systems with time varying delay and linear fractional parametric uncertainties the aim is to design an asymptotically stable fuzzy filter ensuring asymptotical stability and prescribed h performance of the filtering error system for all admissible uncertainties based on the lyapunov krasovskii functional the barbalat lemma and the lmi approach delay dependent sufficient conditions for the solvability of this problem are proposed in terms of lmis and an explicit expression of the desired h fuzzy filter is readily given when these lmis are feasible finally the h filter design problem for a neutral type nonlinear distributed network long line with tunnel diode is considered in the simulation example to demonstrate the effectiveness and applicability of the proposed method

stability analysis of nonlinear multivariable takagi sugeno fuzzy control systems points out how the nonlinearities involved in multivariable takagi sugeno t s fuzzy control systems could originate complex behavior phenomena such as multiple equilibrium points or limit cycles that cannot be detected using conventional stability analysis techniques in the paper the application of mimo frequency domain methods to predict the existence of multiple equilibria and of limit cycles are presented the proposed method is based on the formulation of a lur e problem from the original structure of a t s fuzzy system with a fuzzy controller furthermore this technique makes straightforward the application of input output stability techniques such as the multivariable circle criterion also called the conicity criterion and the harmonic balance method moreover in the paper the application of the harmonic balance method has been generalized to the case of a mimo fuzzy system with asymmetric nonlinearities and improved by the decreasing conservatism a new and more general stability index which could be used to perform a bifurcation analysis of fuzzy control systems is presented the paper includes a collection of examples where the advantages of the proposed approach are made explicit comparing it to the input output conicity criterion and the lyapunov direct method

reflected brownian motion on an orthant we consider a k dimensional diffusion process z whose state space is the nonnegative orthant on the interior of the orthant z behaves like a kdimensional brownian motion with arbitrary covariance matrix and drift vector at each of the k 1 dimensional hyperplanes that form the boundary of the orthant z reflects instantaneously in a direction that is constant over that hyperplane there is no extant theory of multidimensional diffusion that applies to this process because the boundary of its state space is not smooth we adopt an approach that requires a restriction on the directions of reflection but reiman has shown that this restriction is met by all diffusions z arising as heavy traffic limits in open k station queuing networks our process z is defined as a path to path mapping of k dimensional brownian motion from this construction it follows that z is a continuous markov process and a semimartingale using the latter property we obtain a change of variable formula from which one can develop a complete analytical theory for the process z

output feedback lmi tracking control conditions with h criterion for uncertain and disturbed t s models this work concerns the tracking problem of uncertain takagi sugeno t s continuous fuzzy model with external disturbances the objective is to get a model reference based output feedback tracking control law the control scheme is based on a pdc structure a fuzzy observer and a h performance to attenuate the external disturbances the stability of the whole closed loop model is investigated using the well known quadratic lyapunov function the key point of the proposed approaches is to achieve conditions under a lmi linear matrix inequalities formulation in the case of an uncertain and disturbed t s fuzzy model this formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems finally a simulation is provided on the well known inverted pendulum testbed to show the efficiency of the proposed approach

analysis and design for a class of complex control systems part i fuzzy modelling and identification this paper is the first of two dealing with the analysis and design of a class of complex control systems this part deals with fuzzy modelling and identification the second paper is concerned with fuzzy controller design we believe that these two papers show a way to analyze and design complex control systems using a combination of fuzzy logic and modern control theory the complex systems studied in these two papers can be represented by a fuzzy aggregation of a set of local linear models the identification can be divided into two procedures the first procedure is the identification of the membership functions including the determination of the number of fuzzy rules and the estimation of the parameters in the membership functions the second is the identification of the local linear models including the determination of the structure and the parameters of the local rule maps and the global rule interpolation two examples are used to demonstrate the application of the modelling method

on the discrete time bounded real lemma with application in the characterization of static state feedback h controllers abstract this paper deals with the discrete time bounded real lemma and its application in the characterization of all static state feedback h controllers for discrete time systems we first present two versions of the discrete time bounded real lemma the results apply to non minimal stable state space realizations and are given in terms of either the positive semi definite strong solution or the positive semi definite stabilizing solution of a discrete algebraic riccati equation based on the discrete time bounded real lemma we obtain a characterization of all static state feedback h controllers for discrete time systems as an application of the parameterization of all static state feedback h controllers we develop a solution to the discrete time h control problem via static output feedback also a numerical procedure is proposed to determine an output feedback gain

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

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

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

on the critical points of the flight return time function of perturbed closed orbits abstract we deal here with planar analytic systems x x x e which are small perturbations of a period annulus for each transversal section to the unperturbed orbits we denote by t q e the time needed by a perturbed orbit that starts from q to return to we call this the flight return time function we say that the closed orbit of x x x 0 is a continuable critical orbit in a family of the form x x x e if for any q and any that passes through q there exists q e a critical point of t e such that q e q as e 0 in this work we study this new problem of continuability in particular we prove that a simple critical periodic orbit of x x x 0 is a continuable critical orbit in any family of the form x x x e we also give sufficient conditions for the existence of a continuable critical orbit of an isochronous center x x x 0

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

design of state feedback adaptive fuzzy controllers for second order systems using a frequency stability criterion this paper proposes a design method for second order systems that guarantees the stability of an adaptive fuzzy controller with state feedback the system consists of a linear unstable plant the takagi sugeno controller a nonlinear reference model and an adaptation mechanism in this paper gradient based adaptation is used to change the consequents of the controller rules so that the closed loop system behaves like the reference model the proposed method utilizes a frequency domain criterion in the form of the modified circle theorem the controller function is assumed to be a nonlinearity described by a sector condition which means that the function lies between two planes during the process of adaptation this function is verified so it stays in the sector guaranteeing stability the method described here is illustrated by an example of a control system containing an unstable plant with an unknown pole in the right half plane the motivation of this paper is to propose a frequency domain method for the design of state feedback adaptive fuzzy controllers comparing with time domain methods that require advanced software tools the proposed method offers simple graphical interpretation on the nyquist plane