decentralized fuzzy observer based output feedback control for nonlinear large scale systems an lmi approach this paper presents a decentralized fuzzy control problem for asymptotic stabilization of a class of nonlinear large scale systems that use an observer based output feedback scheme a takagi sugeno t s fuzzy model is adopted for the nonlinear large scale system which has unknown interconnection terms and a fuzzy controller is separately considered for measurable and nonmeasurable premise variable cases sufficient conditions are derived for both asymptotic stabilization and optimization of a maximum bound of interconnection and are formulated in terms of linear matrix inequalities finally numerical examples are provided to verify the effectiveness of the proposed techniques

technical communique improvement on observer based h control for t s fuzzy systems this paper provides an improved result over that in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582 for the problem of observer based h control for nonlinear systems in takagi sugeno t s fuzzy model it contributes in three aspects i the present result is less conservative than that in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582 ii the present strict lmi method is a single step approach which overcomes the drawback of a two step approach in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582 iii the matrix dimensions are largely reduced compared with the corresponding ones in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582

new results on monotone dualization and generating hypergraph transversals we consider the problem of dualizing a monotone cnf equivalently computing all minimal transversals of a hypergraph whose associated decision problem is a prominent open problem in np completeness we present a number of new polynomial time respectively output polynomial time results for significant cases which largely advance the tractability frontier and improve on previous results furthermore we show that duality of two monotone cnfs can be disproved with limited nondeterminism more precisely this is feasible in polynomial time with o log2 n log log n suitably guessed bits this result sheds new light on the complexity of this important problem

further studies on h observer design for continuous time takagi sugeno fuzzy model abstract this brief paper is concerned with the problem of observer based h control for nonlinear systems presented by t s takagi sugeno fuzzy models the aim is to reduce the conservatism of finding a smaller h performance index by applying the non quadratic lyapunov function the one step lmis linear matrix inequalities method is applied to design the controller gains and observer gains in addition the initial positions of the observer states are also discussed and an optimization problem is solved to obtain new stable region in the end three examples are given to demonstrate the effectiveness of the proposed approach

asymptotic stability for a linear difference equation with variable delay we shall obtain sufficient conditions for the uniform stability and the global asymptotic stability of the linear difference equation with variable delay xn 1 xn pnxn kn 0 n n where pn is a sequence of nonnegative real numbers kn is a sequence of nonnegative integers and there exists a nonnegative integer k such that kn k for n n

fault detection for t s fuzzy systems with unknown membership functions this paper is concerned with the fault detection fd problem for takagi sugeno t s fuzzy systems with unknown membership functions if the membership functions are unknown the linear fd filter designs with fixed gains have been considered in the literature to reduce the conservatism of the existing results a switching mechanism that depends on the lower and upper bounds of the unknown membership functions is provided to construct an fd filter with varying gains it is shown that the switching type fd filter with varying gains can achieve a better fd performance than the linear fd filter with fixed gains in addition based on some time domain inequalities a novel weighting matrix design approach is introduced to transform the fault sensitivity specification into an h constraint finally two examples are given to show the advantages of the proposed fd method

the complexity of bayesian networks specified by propositional and relational languages abstract we examine the complexity of inference in bayesian networks specified by logical languages we consider representations that range from fragments of propositional logic to function free first order logic with equality in doing so we cover a variety of plate models and of probabilistic relational models we study the complexity of inferences when network query and domain are the input the inferential and the combined complexity when the network is fixed and query and domain are the input the query data complexity and when the network and query are fixed and the domain is the input the domain complexity we draw connections with probabilistic databases and liftability results and obtain complexity classes that range from polynomial to exponential levels we identify new languages with tractable inference and we relate our results to languages based on plates and probabilistic relational models

asymptotic behavior of solutions for neutral difference equations the boundedness and asymptotic behavior of all solutions of the neutral delay difference equation of the form d x n c nx n m p nx n k q nx n l 0 n 0 1 2 are investigated where k l m are positive integers c n q n and p n are three sequences of real numbers the obtained sufficient conditions extend and improve the existing results in the literature

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

the formula isomorphism problem we investigate the computational complexity of the formula isomorphism problem fi on input of two boolean formulas f and g decide whether there exists a permutation of the variables of g such that f and g become equivalent fi is contained in sigma 2 bf p the second level of the polynomial hierarchy our main result is a one round interactive proof for the complementary formula nonisomorphism problem fni where the verifier has access to an np oracle to obtain this we use a result from learning theory by bshouty et al that boolean formulas can be learned probabilistically with equivalence queries and access to an np oracle as a consequence fi cannot be sigma 2 bf p complete unless the polynomial hierarchy collapses further properties of fi are shown fi has and and or functions the counting version fi can be computed in polynomial time relative to fi and fi is self reducible

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

a descriptor representation approach to observer based h control synthesis for discrete time fuzzy systems this work is concerned with the observer based h control synthesis problem of discrete time takagi sugeno t s fuzzy systems with external disturbances the objective is to find a new way to design the controller and observer guaranteeing a prescribed h performance of the fuzzy system by the descriptor representation approach two new conditions for observer based h control synthesis are proposed based on various lyapunov function candidates which are in the form of linear matrix inequalities lmis a numerical example will be given to show the efficiency of the proposed method

design of observer based h_ infty control for fuzzy time delay systems this paper addresses the problem of observer based hinfin control for nonlinear systems with time varying delay represented by takagi sugeno t s fuzzy model it presents a single step linear matrix inequality lmi method for the fuzzy control design which overcomes the drawback of the two step lmi approach often encountered in the literature the derivation relies mainly on a proposed matrix decoupling technique using which a resultant matrix inequality can be equivalently converted to strict lmis when restricted to delay free fuzzy systems the present results improve or reduce to existing ones illustrative examples show the effectiveness and merits of the present results

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

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

global asymptotic stability for nonlinear difference equations in this paper some sufficient conditions are established for the asymptotic stability of solutions of the nonlinear difference equationx n 1 x n a nx n k b nf x n l n 0 which generalize and improve some exist results in the literature

global attractivity of neutral difference equations abstract in this paper we discuss the global attractivity of the neutral difference equation n c n k p n n l 0 n 0 1 2 where is the forward difference operator c 1 1 k l and pn is a sequence of nonnegative real numbers

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

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

a novel observer based output feedback controller design for discrete time fuzzy systems this paper addresses the problem of observer based output feedback controller designs for discrete time t s fuzzy systems based on a relaxed approach in which the fuzzy lyapunov functions are used different from the existing two step method a single step linear matrix inequality method is provided for the observer based controller design it is shown that the controller and observer parameters can be obtained by solving a set of strict linear matrix inequalities that are numerically feasible with commercially available software the new design method not only overcomes the drawback induced by the two step approach but also provides less conservative results over some existing results finally the effectiveness of the proposed approach is demonstrated by an example

complexity of dnf minimization and isomorphism testing for monotone formulas we investigate the complexity of finding prime implicants and minimum equivalent dnfs for boolean formulas and of testing equivalence and isomorphism of monotone formulas for dnf related problems the complexity of the monotone case differs strongly from the arbitrary case we show that it is dp complete to check whether a monomial is a prime implicant for an arbitrary formula but the equivalent problem for monotone formulas is in l we show pp completeness of checking if the minimum size of a dnf for a monotone formula is at most k and for k in unary we show that the complexity of the problem drops to conp in christopher umans christopher umans the minimum equivalent dnf problem and shortest implicants journal of computer and system sciences 63 4 2001 597 611 a similar problem for arbitrary formulas was shown to be 2 p complete we show that calculating the minimum equivalent dnf for a monotone formula is possible in output polynomial time if and only if p np finally we disprove a conjecture from steffen reith steffen reith on the complexity of some equivalence problems for propositional calculi in proceedings of the 28th international symposium on mathematical foundations of computer science mfcs vol 2747 lecture notes in computer science springer 2003 pp 632 641 by showing that checking whether two formulas are isomorphic has the same complexity for arbitrary formulas as for monotone formulas

nonquadratic cal h _ infty stabilization conditions for observer based t s fuzzy control systems this paper investigates the nonquadratic output feedback stabilization problem for nonlinear systems in takagi sugeno s t s form to achieve improved performance in the cal h infty sense this paper provides two kinds of relaxation techniques one for the case where all premise variables are measurable and one for the case where the premise variables are immeasurable in particular the emphasis of the second technique is the use of estimated premise variables for nonquadratic lyapunov functions

identifying the minimal transversals of a hypergraph and related problems the paper considers two decision problems on hypergraphs hypergraph saturation and recognition of the transversal hypergraph and discusses their significance for several search problems in applied computer science hypergraph saturation i e given a hypergraph cal h decide if every subset of vertices is contained in or contains some edge of cal h is shown to be co np complete a certain subproblem of hypergraph saturation the saturation of simple hypergraphs i e sperner families is shown to be under polynomial transformation equivalent to transversal hypergraph recognition i e given two hypergraphs cal h 1 cal h 2 decide if the sets in cal h 2 are all the minimal transversals of cal h 1 the complexity of the search problem related to the recognition of the transversal hypergraph the computation of the transversal hypergraph is an open problem this task needs time exponential in the input size it is unknown whether an output polynomial algorithm exists for several important subcases for instance if an upper or lower bound is imposed on the edge size or for acyclic hypergraphs output polynomial algorithms are presented computing or recognizing the minimal transversals of a hypergraph is a frequent problem in practice which is pointed out by identifying important applications in database theory boolean switching theory logic and artificial intelligence ai particularly in model based diagnosis

h_ infty filter design for nonlinear systems with time delay through t s fuzzy model approach this paper is concerned with the hinfin filter design for nonlinear systems with time varying delay via takagi sugeno fuzzy model approach delay dependent design method is proposed in terms of linear matrix inequalities lmis which forms the main contribution of this paper the main technique used is the free weighting matrix method combined with a matrix decoupling approach the results for rate independent case delay independent case and delay free case are also given as easy corollaries an illustrative example is given to show the effectiveness of the present method

piecewise fuzzy anti windup dynamic output feedback control of nonlinear processes with amplitude and rate actuator saturations in this paper a novel anti windup dynamic output compensator is developed to deal with the robust h infin output feedback control problem of nonlinear processes with amplitude and rate actuator saturations and external disturbances via fuzzy modeling of nonlinear systems the proposed piecewise fuzzy anti windup dynamic output feedback controller is designed based on piecewise quadratic lyapunov functions it is shown that with sector conditions robust output feedback stabilization of an input constrained nonlinear process can be formulated as a convex optimization problem subject to linear matrix inequalities simulation study on a strongly nonlinear continuously stirred tank reactor cstr benchmark plant is given to show the performance of the proposed anti windup dynamic compensator

robust h h fault detection observer design for descriptor lpv systems with unmeasurable gain scheduling functions this paper addresses a design of a fault detection observer fdo for descriptor linear parameter varying d lpv systems in contrast with the conventional approach for d lpv systems the gain scheduling functions gsf are considered unmeasurable the fdo is investigated in the h h index framework in order to minimise the effects of the disturbance and maximise the effect of faults on the residuals and minimise the error caused by the unmeasurable gsf the stability is guaranteed based on a lyapunov approach sufficient conditions for the existence of the fdo are established in terms of linear matrix inequalities the effectiveness of the proposed method is illustrated by means of a simulation example

stability and stabilization of delayed t s fuzzy systems a delay partitioning approach this paper proposes a new approach namely the delay partitioning approach to solving the problems of stability analysis and stabilization for continuous time delay takagi sugeno fuzzy systems based on the idea of delay fractioning a new method is proposed for the delay dependent stability analysis of fuzzy time delay systems due to the instrumental idea of delay partitioning the proposed stability condition is much less conservative than most of the existing results the conservatism reduction becomes more obvious with the partitioning getting thinner based on this the problem of stabilization via the so called parallel distributed compensation scheme is also solved both the stability and stabilization results are further extended to time delay fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities lmis which can be readily solved via standard numerical software the advantage of the results proposed in this paper lies in their reduced conservatism as shown via detailed illustrative examples the idea of delay partitioning is well demonstrated to be efficient for conservatism reduction and could be extended to solving other problems related to fuzzy delay systems

technical communique observer based h fuzzy control design for t s fuzzy systems with state delays this paper is concerned with the problem of observer based h fuzzy control design for takagi sugeno t s fuzzy systems with time delay the main contribution is that an effective matrix decoupling technique is developed to derive a single step lmi condition for observer based h control design this overcomes the drawback of two step lmi approach in the literature when restricted to delay free fuzzy systems the present result is shown less conservative than existing ones an illustrative example is given to show the effectiveness of our results

global asymptotic stability in a nonlinear nonautonomous difference equation with delays abstract in this paper some sufficient conditions are obtained for the global asymptotic stability of a nonlinear nonautonomous difference equation with delays and the works in 1 and the authors 2 are generalized

an approach to observer design of continuous time takagi sugeno fuzzy model with bounded disturbances this paper addresses the problem of designing the observer for a class of nonlinear systems by using the t s takagi sugeno fuzzy model first two lemmas are obtained to demonstrate how to design the observer then based on the non quadratic lyapunov function a new method is proposed to locally stabilize the t s fuzzy system the new method can be applied to any t s models no matter whether the rules are even or odd naturally the new method is extended to get some lmis linear matrix inequalities to design the observer for practical reason the disturbances considered in this paper are bounded by magnitude and energy finally three examples are given to illustrate the effectiveness of the new approach