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

design of fuzzy control systems with guaranteed stability abstract this paper addresses the analysis and design of fuzzy control systems the fuzzy systems are represented by a family of local state space models with aggregation the controller is designed by considering each local state feedback controller and a compensating controller the compensating controller is based on the well known variable structure control theory it is shown that this controller guarantees global stability of the closed loop fuzzy system the issues of a state observer for the fuzzy system is also addressed a numerical example and an example of nonlinear system control are given for demonstration of the performance of the method

on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

fault detection for uncertain fuzzy systems an lmi approach this paper studies the problem of designing a robust fault detection system for uncertain takagi sugeno fuzzy models the worst case fault sensitivity measure is formulated in terms of linear matrix inequalities the existence of a robust fault detection system that guarantees i the l2 gain from a fault signal to a residual signal greater than a prescribed value and ii the l2 gain from an exogenous input to a residual signal less than a prescribed value is given in terms of the solvability of linear matrix inequalities numerical examples are used to illustrate the effectiveness of the proposed design techniques

block pickard models for two dimensional constraints in pickard random fields prf the probabilities of finite configurations and the entropy of the field can be calculated explicitly but only very simple structures can be incorporated into such a field given two markov chains describing a boundary an algorithm is presented which determines whether a prf consistent with the distribution on the boundary and a 2 d constraint exists iterative scaling is used as part of the algorithm which also determines the conditional probabilities yielding the maximum entropy for the given boundary description if a solution exists a prf is defined for the domino tiling constraint represented by a quaternary alphabet prf models are also presented for higher order constraints including the no isolated bits n i b constraint and a minimum distance 3 constraint by defining super symbols on blocks of binary symbols

free products of compact quantum groups we construct and study compact quantum groups from free products ofc algebras in this connection we discover two mysterious classes of natural compact quantum groups a u m anda o m thea u m s respectivelya o m s are non isomorphic to each other for differentm s and are not obtainable by the ordinary quantization method we also clarify some basic concepts in the theory of compact quantum groups

lmi based stability analysis for fuzzy model based control systems using artificial t s fuzzy model this paper investigates the stability of fuzzy model based fmb control systems an alternative stability analysis approach using an artificial fuzzy system based on the lyapunov stability theory is proposed to facilitate the stability analysis the continuous membership functions of the takagi sugeno t s fuzzy model are represented by the staircase ones with the nice property of the staircase membership functions it turns the set of infinite number of linear matrix inequality lmi based stability conditions into a finite one furthermore the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions the stability of the original fmb control systems is guaranteed by the satisfaction of the lmi based stability conditions the proposed stability analysis is applied to the fmb control systems of which the t s fuzzy model and fuzzy controller do not share the same premise membership functions and thus is able to enhance the design flexibility of the fuzzy controller a simulation example is given to illustrate the merits of the proposed approach

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

output regulation of polynomial fuzzy model based control systems this paper investigates the output regulation problem of polynomial fuzzy model based pfmb control systems with the consideration of system stability and control synthesis using the sum of squares sos based approach a pfmb control system is formed by a polynomial fuzzy model and a polynomial fuzzy controller with integral action connected in a closed loop three cases of pfmb control systems regarding the premise membership functions and number of fuzzy rules which have their own properties and advantages are considered the stability of the pfmb control systems is investigated based on the lyapunov stability theory with consideration of the information of membership functions sos based stability conditions corresponding to each case are obtained to guarantee system stability and to realize output regulation simulation examples are given to compare the three cases and illustrate the effectiveness of the proposed approach

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

robust design of rule based fuzzy controllers this paper deals with the design of stable and robust rule based fuzzy control systems new expressions to compute indices which provide a measure of the stability and robustness of fuzzy control systems are presented the relation between the modification of the rules and the stability is studied through the so called sensitivity indices the paper presents procedures that make use of these indices to improve the design of fuzzy control systems including the modification of the rules to obtain the global stability of an unstable system with multiple attractors and to improve the dynamic behavior or the robustness of a non linear plant an example with a fuzzy controller for a system with non linear damping and saturation in the actuation is presented to illustrate the design procedure

h output feedback control of fuzzy system models under sampled measurements this paper studies the problem of control for a class of fuzzy system models by using a linear output controller the system under consideration is described by a continuous time fuzzy system model under sampled output measurements the premise variables of the fuzzy system model are assumed unmeasurable we develop a technique for designing an output feedback control law which globally stabilises this class of fuzzy system models a design algorithm for constructing the linear output controller is given a numerical simulation example is given to show the potential of the proposed techniques

stability analysis and performance design for fuzzy model based control system under imperfect premise matching this paper investigates the stability analysis and performance design of nonlinear systems to facilitate the stability analysis the takagi sugeno t s fuzzy model is employed to represent the nonlinear plant under the imperfect premise matching in which t s fuzzy model and fuzzy controller do not share the same membership functions a fuzzy controller with enhanced design flexibility and robustness property is proposed to control the nonlinear plant however the nice characteristic given by the perfect premise matching leading to conservative stability conditions vanishes in this paper under the imperfect premise matching information of membership functions of the fuzzy model and controller are considered in stability analysis with the introduction of slack matrices relaxed linear matrix inequality lmi based stability conditions are derived using lyapunov based approach furthermore lmi based performance conditions are provided to guarantee system performance simulation examples are given to illustrate the effectiveness of the proposed approach

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

fuzzy controller with stability and performance rules for nonlinear systems this paper presents a fuzzy controller which can be designed through two steps for nonlinear systems the proposed fuzzy controller consists of two groups of fuzzy rules namely the stability and performance rules stability conditions which involve the stability rules only will be derived to guarantee the system stability by properly designing the shapes of the membership functions of the fuzzy controller the stability conditions can be relaxed the proposed fuzzy controller offers a property that the performance rules will not alter the system stability this favorable property enables the performance rules to be designed freely to achieve the system performance without affecting the system stability consequently the system stability and performance can be designed in two separate processes an application example will be presented to show the merits of the proposed approach

the haagerup property for locally compact quantum groups the haagerup property for locally compact groups is generalised to the context of locally compact quantum groups with several equivalent characterisations in terms of the unitary representations and positive definite functions established in particular it is shown that a locally compact quantum group g has the haagerup property if and only if its mixing representations are dense in the space of all unitary representations for discrete g we characterise the haagerup property by the existence of a symmetric proper conditionally negative functional on the dual quantum group hat g by the existence of a real proper cocycle on g and further if g is also unimodular we show that the haagerup property is a von neumann property of g this extends results of akemann walter bekka cherix valette and jolissaint to the quantum setting and provides a connection to the recent work of brannan we use these characterisations to show that the haagerup property is preserved under free products of discrete quantum groups

technical communique fuzzy h output feedback control of nonlinear systems under sampled measurements this paper studies the problem of designing an h fuzzy feedback control for a class of nonlinear systems described by a continuous time fuzzy system model under sampled output measurements the premise variables of the fuzzy system model are allowed to be unavailable we develop a technique for designing an h fuzzy feedback control that guarantees the l 2 gain from an exogenous input to a controlled output is less than or equal to a prescribed value a design algorithm for constructing the h fuzzy feedback controller is given

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

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

ccap for universal discrete quantum groups we show that the discrete duals of the free orthogonal quantum groups have the haagerup property and the completely contractive approximation property analogous results hold for the free unitary quantum groups and the quantum automorphism groups of finite dimensional c algebras the proof relies on the monoidal equivalence between free orthogonal quantum groups and su q 2 quantum groups on the construction of a sufficient supply of bounded central functionals for su q 2 quantum groups and on the free product techniques of ricard and xu our results generalize previous work in the kac setting due to brannan on the haagerup property and due to the second author on the ccap

on the ell 2 betti numbers of universal quantum groups we show that the first ell 2 betti number of the duals of the free unitary quantum groups is one and that all ell 2 betti numbers vanish for the duals of the quantum automorphism groups of full matrix algebras

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

stability analysis and design for a class of continuous time fuzzy control systems this paper presents a design method for a class of fuzzy control systems the class of fuzzy systems considered can be represented by the takagi sugeno fuzzy model which is a type of dynamic fuzzy model a constructive algorithm is developed to obtain the stabilizing feedback control law for the system the main contribution of this paper is the development of an equivalent principle that is the design of a fuzzy control system is equivalent to the design of a set of linear time invariant extreme systems thus any design method in linear control system theory can be used to design a fuzzy control system an example is given to illustrate the application of the method

stable adaptive control of fuzzy dynamic systems this paper discusses fuzzy model reference adaptive control for a class of nonlinear systems the system concerned is represented by a family of local transfer function models smoothly connected together by fuzzy membership functions the model reference adaptive control law is first designed in each local region and then constructed in global domain it is shown that the resulting fuzzy adaptive control system is globally stable based on a suitable piecewise differentiable lyapunov function a simulation example is given for demonstration of the application of the method

orthogonal free quantum group factors are strongly 1 bounded abstract we prove that the orthogonal free quantum group factors l f o n are strongly 1 bounded in the sense of jung in particular they are not isomorphic to free group factors this result is obtained by establishing a spectral regularity result for the edge reversing operator on the quantum cayley tree associated to f o n and combining this result with a recent free entropy dimension rank theorem of jung and shlyakhtenko

a new error estimation approach based on fuzzy logic system for h r adaptive boundary element method abstract conventional adaptive boundary element method cannot be universally applied to solve many more problems than the subject it discussed and different error estimation formulas need to be designed for varied problems this paper put forward a new error analysis method based on the fuzzy logic system which is able to make error estimation effectively using human expert experience and solve the two classical elasticity problems in conjunction with the h r adaptive boundary element method numerical examples have illustrated the effectiveness superiority and potential of a fuzzy logic approach in the adaptive boundary element method

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

the full classification of orthogonal easy quantum groups we study easy quantum groups a combinatorial class of orthogonal quantum groups introduced by banica speicher in 2009 we show that there is a countable descending chain of easy quantum groups interpolating between bichon s free wreath product with the permutation group s n and a semi direct product of a permutation action of s n on a free product this reveals a series of new commutation relations interpolating between a free product construction and the tensor product furthermore we prove a dichotomy result saying that every hyperoctahedral easy quantum group is either part of our new interpolating series of quantum groups or belongs to a class of semi direct product quantum groups recently studied by the authors this completes the classification of easy quantum groups we also study combinatorial and operator algebraic aspects of the new interpolating series

the boundary of universal discrete quantum groups exactness and factoriality we study the c algebras and von neumann algebras associated with the universal discrete quantum groups they give rise to full prime factors and simple exact c algebras the main tool in our work is the study of an amenable boundary action yielding the akemann ostrand property finally this boundary can be identified with the martin or the poisson boundary of a quantum random walk

analysis and design of fuzzy reduced dimensional observer and fuzzy functional observer on the basis of the t s fuzzy model this paper discusses the following three problems the fuzzy reduced dimensional observer the general structure of the fuzzy observer the fuzzy functional observer for both the continuous and discrete case respectively the separation property that is the fuzzy controller and the fuzzy observer can be independently designed is also addressed the numerical simulation and the experiment on an inverted pendulum system are given to illustrate the soundness of these results

symmetries of levy processes on compact quantum groups their markov semigroups and potential theory quantum markov semigroups qms i e strongly continuous semigroups of unital completely positive maps on compact quantum groups are studied we show that translation invariant qmss on the universal or reduced c algebra of a compact quantum group are in one to one correspondence with levy processes on its hopf algebra we use the theory of levy processes on involutive bialgebras to characterize symmetry properties of the associated qms it turns out that the qms is self adjoint resp kms symmetric if and only if the generating functional of the levy process is invariant under the antipode resp the unitary antipode furthermore we study levy processes whose marginal states are invariant under the adjoint action finally some related aspects of the potential theory as dirichlet form derivation and spectral triple are investigated we discuss how the above results apply to compact groups group c algebras of discrete groups free orthogonal quantum groups on and twisted suq 2 quantum group

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

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

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

stable fuzzy adaptive control for a class of nonlinear systems abstract in this paper two adaptive fuzzy control schemes for a class of nonlinear systems are proposed each scheme employs a fuzzy control with an adaptive law and a compensation control it is proved that the closed loop system is asymptotically stable based on lyapunov synthesis approach while the identification of the controlled plant is unnecessary finally these schemes are applied to control a chaotic system the simulation results show that our schemes are superior to the scheme of 12

h state feedback control for fuzzy systems with input saturation via fuzzy weighting dependent lyapunov functions this paper proposes a method for designing an h state feedback fuzzy controller for discrete time takagi sugeno t s fuzzy systems with input saturation to address the input saturation problem this paper first formulates a set invariance condition for the t s fuzzy systems then based on the set invariance condition this paper establishes h stabilization conditions associated with a fuzzy weighting dependent lyapunov function where the fuzzy controller is designed to be dependent on not only the current time but also the one step past information on the time varying fuzzy weighting functions in the derivation the h stabilization conditions are first formulated in terms of parameterized linear matrix inequalities plmis and then reconverted into lmis by an efficient relaxation technique

local characteristics entropy and limit theorems for spanning trees and domino tilings via transfer impedances let g be a finite graph or an infinite graph on which mathbb z d acts with finite fundamental domain if g is finite let mathbf t be a random spanning tree chosen uniformly from all spanning trees of g if g is infinite methods from pemantle show that this still makes sense producing a random essential spanning forest of g a method for calculating local characteristics i e finite dimensional marginals of mathbf t from the transfer impedance matrix is presented this differs from the classical matrix tree theorem in that only small pieces of the matrix n dimensional minors are needed to compute small n dimensional marginals calculation of the matrix entries relies on the calculation of the green s function for g which is not a local calculation however it is shown how the calculation of the green s function may be reduced to a finite computation in the case when g is an infinite graph admitting a z d action with finite quotient the same computation also gives the entropy of the law of mathbf t these results are applied to the problem of tiling certain lattices by dominos the so called dimer problem another application of these results is to prove modified versions of conjectures of aldous on the limiting distribution of degrees of a vertex and on the local structure near a vertex of a uniform random spanning tree in a lattice whose dimension is going to infinity included is a generalization of moments to tree valued random variables and criteria for these generalized moments to determine a distribution

cut off phenomenon for random walks on free orthogonal quantum groups we give bounds in total variation distance for random walks associated to pure central states on free orthogonal quantum groups as a consequence we prove that the analogue of the uniform plane kac walk on this quantum group has a cut off at n ln n 2 1 cos theta this is the first result of this type for genuine compact quantum groups we also obtain similar results for mixtures of rotations and quantum permutations

free wreath product quantum groups the monoidal category approximation properties and free probability in this paper we find the fusion rules of the free wreath product quantum groups g sn for all compact matrix quantum groups of kac type g and n 4 this is based on a combinatorial description of the intertwiner spaces between certain generating representations of g sn the combinatorial properties of the intertwiner spaces in g sn allow us to obtain several probabilistic applications we prove also the monoidal equivalence between g sn and a compact quantum group whose dual is a discrete quantum subgroup of the free product g suq 2 for some 0 q 1 we obtain as a corollary certain stability results for the operator algebras associated with the free wreath products of quantum groups such as the acpap property and exactness

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

the connes embedding property for quantum group von neumann algebras for a compact quantum group g of kac type we study the existence of a haar trace preserving embedding of the von neumann algebra l g into an ultrapower of the hyperfinite ii 1 factor the connes embedding property for l g we establish a connection between the connes embedding property for l g and the structure of certain quantum subgroups of g and use this to prove that the ii 1 factors l o n and l u n associated to the free orthogonal and free unitary quantum groups have the connes embedding property for all n 4 as an application we deduce that the free entropy dimension of the standard generators of l o n equals 1 for all n 4 we also mention an application of our work to the problem of classifying the quantum subgroups of o n

fusion semi rings arising from quantum groups abstract we study the fusion semirings arising from easy quantum groups we classify all the possible free ones answering a question of t banica and r vergnioux these are exactly the fusion rings of quantum groups without any nontrivial one dimensional representation we then classify the possible groups of one dimensional representations for general easy quantum groups associated to noncrossing partitions as an application we give a unified proof of the haagerup property for a broad class of easy quantum groups recovering as special cases previous results by m brannan and f lemeux we end with some considerations on the description of the full fusion ring in the general case

universal fuzzy controllers for a class of nonlinear systems in this paper we address the issues of universal fuzzy controllers we first present a universal function approximation theorem based on a fuzzy dynamic model then we show the results of universal fuzzy controllers for a large class of nonlinear systems

examples of weakly amenable discrete quantum groups abstract we prove that the free orthogonal and free unitary quantum groups f o n and f u n are weakly amenable and that their cowling haagerup constant is equal to 1 this is achieved by estimating the completely bounded norm of the projections on the coefficients of irreducible representations of their compact duals an argument of monoidal equivalence then allows us to extend this result to quantum automorphism groups of finite spaces and even yields some examples of weakly amenable non unimodular discrete quantum groups with the haagerup property

the radial masa in free orthogonal quantum groups abstract we prove that the radial subalgebra in free orthogonal quantum group factors is maximal abelian and mixing and we compute the associated bimodule the proof relies on new properties of the jones wenzl projections and on an estimate of certain scalar products of coefficients of irreducible representations

a systematic study of fuzzy pid controllers function based evaluation approach a function based evaluation approach is proposed for a systematic study of fuzzy proportional integral derivative pid like controllers this approach is applied for deriving process independent design guidelines from addressing two issues simplicity and nonlinearity to examine the simplicity of fuzzy pid controllers we conclude that direct action controllers exhibit simpler design properties than gain scheduling controllers then we evaluate the inference structures of direct action controllers in five criteria control action composition input coupling gain dependency gain role change and rule parameter growth three types of fuzzy pid controllers using one two and three input inference structures are analyzed the results according to the criteria demonstrate some shortcomings in mamdani s two input controllers for keeping the simplicity feature like a linear pid controller a one input fuzzy pid controller with one to three mapping inference engine is recommended we discuss three evaluation approaches in a nonlinear approximation study function estimation based generalization capability based and nonlinearity variation based approximations the study focuses on the last approach a nonlinearity evaluation is then performed for several one input fuzzy pid controllers based on two measures nonlinearity variation index and linearity approximation index using these quantitative indices one can make a reasonable selection of fuzzy reasoning mechanisms and membership functions without requiring any process information from the study we observed that the zadeh mamdani s max min gravity scheme produces the highest score in terms of nonlinearity variations which is superior to other schemes such as mizumoto s product sum gravity and takagi sugeno kang schemes

relaxed stability and stabilization conditions for a t s fuzzy discrete system it is known that the stability condition of a t s fuzzy discrete system depends on the existence of the common matrix p which satisfies all lyapunov inequalities in general the common matrix p can be found by means of linear matrix inequalities lmi method however if the number of rules of a fuzzy system is large the common matrix p may not exist or may not be found even using lmi therefore in this paper the state space is divided into several subregions and the local common matrix p j for each subregion j is found then the number of lyapunov inequalities to be satisfied by the corresponding local common matrix p j becomes much fewer such that the stability condition of the fuzzy system is more relaxed the similar derivation is also extended to solve the stabilization problem of the t s fuzzy discrete system with parallel distributed compensation

design of robust fuzzy model based controller with sliding mode control for siso nonlinear systems in this paper we present the design of a new type of fuzzy controllers for controlling complex single input single output systems by incorporating sliding mode control theory with fuzzy control technology first a fuzzy model of the given nonlinear system is constructed to represent the local dynamic behaviors of the given nonlinear system a global controller is then constructed by combining all local state feedback controllers and a global supervisory sliding mode controller improved robustness and tracking performance are obtained by a seamless integration of fuzzy model based control and sliding mode control in addition stability of controlling the original underlying nonlinear systems is guaranteed owing to the robustness of the sliding mode control method to system parameter uncertainties two simulation examples are included to show the effectiveness and feasibility of the developed integrated controller

stochastic aspects of easy quantum groups we consider several orthogonal quantum groups satisfying the easiness assumption axiomatized in our previous paper for each of them we discuss the computation of the asymptotic law of tr uk with respect to the haar measure u being the fundamental representation for the classical groups on sn we recover in this way some well known results of diaconis and shahshahani

mamdani type fuzzy controllers are universal fuzzy controllers abstract this paper addresses the issues of universal fuzzy controllers and shows that the mamdani type fuzzy controllers are universal fuzzy controllers furthermore a constructive procedure is also presented to obtain the universal fuzzy controller if the reference fuzzy model is given

amenability and co amenability of algebraic quantum groups ii abstract we continue our study of the concepts of amenability and co amenability for algebraic quantum groups in the sense of a van daele and our investigation of their relationship with nuclearity and injectivity one major tool for our analysis is that every non degenerate representation of the universal c algebra associated to an algebraic quantum group has a unitary generator which may be described in a concrete way

robustness design of time delay fuzzy systems using fuzzy lyapunov method abstract in this study we address a fuzzy lyapunov method for the stability analysis of time delay fuzzy systems subject to external disturbances a takagi sugeno t s fuzzy model and parallel distributed compensation pdc scheme are first employed to design a nonlinear fuzzy controller for the stabilization of time delay fuzzy systems according to the controlled system the h criterion is derived based on the fuzzy lyapunov method which is defined in terms of fuzzy blending quadratic lyapunov functions based on the stability criterion the time delay fuzzy systems are guaranteed to be stable the control problem can then be reformulated as a linear matrix inequality lmi problem a simulation is provided to explore the feasibility of the proposed fuzzy controller design method

robust h nonlinear modeling and control via uncertain fuzzy systems in theory an algebraic riccati equation are scheme applicable to robust h quadratic stabilization problems of a class of uncertain fuzzy systems representing a nonlinear control system is investigated it is proved that existence of a set of solvable ares suffices to guarantee the quadratic stabilization of an uncertain fuzzy system while satisfying h norm bound constraint it is also shown that a stabilizing control law is reminiscent of an optimal control law found in linear quadratic regulator and a linear control law can be immediately discerned from the stabilizing one in practice the minimal solution to a set of parameter dependent ares is somewhat stringent and instead a linear matrix inequalities formulation is suggested to search for a feasible solution to the associated ares the proposed method is compared with the existing fuzzy literature from various aspects

the fusion rules of some free wreath product quantum groups and applications abstract in this article we find the fusion rules of the free wreath product quantum groups s n for any discrete group to do this we describe the spaces of intertwiners between basic corepresentations which allows us to identify the irreducible corepresentations we then apply the knowledge of the fusion rules to prove in most cases several operator algebraic properties of the associated reduced c algebras such as simplicity and uniqueness of the trace we also prove that the associated von neumann algebra is a full type ii 1 factor and that the dual of s n has the haagerup approximation property for all finite groups

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

decoupled fuzzy controller design with single input fuzzy logic a decoupled fuzzy controller design with single input fuzzy logic is proposed we will utilize the approach of the single input fuzzy logic to explore the fourth order nonlinear systems in addition five fuzzy rules are given to control a class of fourth order nonlinear systems using this approach the system can achieve asymptotic stability and the response of system will converge faster than that of previous reports two simulation studies of a cart pole system and a ball beam system are presented to demonstrate the effectiveness of the method

stationary markov random fields on a finite rectangular lattice this paper provides a complete characterization of stationary markov random fields on a finite rectangular non toroidal lattice in the basic case of a second order neighborhood system equivalently it characterizes stationary markov fields on z sup 2 whose restrictions to finite rectangular subsets are still markovian i e even on the boundaries until now pickard random fields formed the only known class of such fields first we derive a necessary and sufficient condition for markov random fields on a finite lattice to be stationary it is shown that their joint distribution factors in terms of the marginal distribution on a generic 2 spl times 2 cell which must fulfil some consistency constraints second we solve the consistency constraints and provide a complete characterization of such measures in three cases symmetric measures and gaussian measures are shown to necessarily belong to the pickard class whereas binary measures belong either to the pickard class or to a new nontrivial class which is further studied in particular the corresponding fields admit a simple parameterization and may be simulated in a simple although nonunilateral manner

robust fuzzy h control for uncertain nonlinear systems via state feedback an lmi approach this paper presents a method for designing robust fuzzy h controllers which stabilize nonlinear systems and guarantee an induced l2 norm bound constraint on disturbance attenuation for all admissible uncertainties takagi and sugeno fuzzy models with uncertainties are used as the model for the uncertain nonlinear systems fuzzy control systems utilize the concept of the so called parallel distributed compensation pdc using a single quadratic lyapunov function the stability with decay rate and disturbance attenuation for takagi and sugeno fuzzy model with parameter uncertainties are discussed a sufficient condition for the presence of the robust fuzzy h controllers is then presented in terms of linear matrix inequalities lmis finally design examples of robust fuzzy h controllers for uncertain nonlinear systems are presented

on the classification of easy quantum groups abstract in 2009 banica and speicher began to study the compact quantum groups g with s n g o n whose intertwiner spaces are induced by some partitions these so called easy quantum groups have a deep connection to combinatorics we continue their work on classifying these objects by introducing some new examples of easy quantum groups in particular we show that the six easy groups o n s n h n b n s n and b n split into seven cases o n s n h n b n s n b n and b n on the side of free easy quantum groups also we give a complete classification in the half liberated and in the nonhyperoctahedral case

an approach to h control of fuzzy dynamic systems this paper presents an approach to h control of a class of continuous time nonlinear systems which can be represented by a fuzzy dynamic model a suitable piecewise differentiable quadratic lyapunov function is used to establish asymptotic stability and h performance of the closed loop fuzzy control system a constructive algorithm is developed to obtain the h feedback control law which involves solving a set of suitable algebraic riccati equations an example is given to illustrate the application of the method

asymptotic infinitesimal freeness with amalgamation for haar quantum unitary random matrices we consider the limiting distribution of u na nu n and bn and more general expressions where an and bn are n n matrices with entries in a unital c algebra mathcal b which have limiting mathcal b valued distributions as n and un is a n n haar distributed quantum unitary random matrix with entries independent from mathcal b under a boundedness assumption we show that u na nu n and bn are asymptotically free with amalgamation over mathcal b moreover this also holds in the stronger infinitesimal sense of belinschi shlyakhtenko

a linear output structure for fuzzy logic controllers in this paper the output structure of multiple input single output fuzzy logic controller flcr is studied the input and output variables of the flcr are all characterized by normal triangular shaped membership functions and fuzzy partitions are considered for corresponding universes of discourse a special mapping linear rule mapping fuzzy sets and systems 57 1993 149 which describes the relationship between the input variables and the output variables of one rule is used the conclusion proposed is that the output of multiple input single output flcr can be represented by the convex linear combination of its crisp input variables a precise mathematical model of flcr which is helpful to analyze fuzzy control and tune the fuzzy logic controller is given

fuzzy incremental control algorithm of loop heat pipe cooling system for spacecraft applications reliable and high precision thermal control technologies are essential for the safe flight of advanced spacecraft a fuzzy incremental control strategy is proposed for control of an lhp space cooling system comprising a loop heat pipe and a variable emittance radiator with mems louver the generating and performing algorithm of the fuzzy control rules is provided with an analytical form based on the understanding of dynamics and control mechanisms of the space cooling system this paper also presents a novel integrated mathematical model for the dynamic analysis of the lhp space cooling system and a numerical evaluation of the investigated control schemes numerical simulation results on the closed loop control effects suggest that the proposed control strategy takes advantage of no steady error small overshoots and short settling times thus benefiting safe highly accurate and reliable operation of the entire space cooling system the overshoots of the most important operating parameters t o b q r and p under the proposed fuzzy incremental control have been reduced to 16 3 17 6 and 18 6 of the compared pid control s while the respective settling times have been shortened to 33 9 42 3 and 30 5 of the reference values

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

comparison of unitary duals of drinfeld doubles and complex semisimple lie groups we determine a substantial part of the unitary representation theory of the drinfeld double of a q deformation of a compact lie group in terms of the complexification of the compact lie group using this we show that the dual of every q deformation of a higher rank compact lie group has central property t we also determine the unitary dual of sl q n mathbb c

the haagerup approximation property for von neumann algebras via quantum markov semigroups and dirichlet forms the haagerup approximation property for a von neumann algebra equipped with a faithful normal state is shown to imply existence of unital preserving and kms symmetric approximating maps this is used to obtain a characterisation of the haagerup approximation property via quantum markov semigroups extending the tracial case result due to jolissaint and martin and further via quantum dirichlet forms

designing fuzzy controllers from a variable structures standpoint a procedure is presented for designing fuzzy controllers based upon variable structures techniques three such controllers are presented the fuzzy equivalents of sliding mode controllers saturating controllers and tanh controllers by using an approach based upon variables structures vss techniques the stability of each of these controllers is assured by using a sliding surface the order of the rule base is reduced to size r spl times m where r is the number of inputs and m is the number of fuzzification levels this combination makes the proposed design procedure able to generate simple controllers with guaranteed stability properties to illustrate the proposed design procedure fuzzy controllers are designed for a ball and beam system it is demonstrated that in spite of this system being a fourth order unstable system the proposed design procedure results in simple stable fuzzy controllers

paths in quantum cayley trees and l 2 cohomology abstract we study existence uniqueness and triviality of path cocycles in the quantum cayley graph of universal discrete quantum groups in the orthogonal case we find that the unique path cocycle is trivial in contrast with the case of free groups where it is proper in the unitary case it is neither bounded nor proper from this geometrical result we deduce the vanishing of the first l 2 betti number of a o i n

sos based stability analysis of polynomial fuzzy model based control systems via polynomial membership functions this paper presents stability analysis of polynomial fuzzy model based fmb control systems using the sum of squares sos approach recently stability analysis of the polynomial fuzzy control systems which is a generalized form of the well known takagi sugeno t s fmb control systems has been reported in the form of sos based stability conditions lack of information on the relations between membership functions and premise variables in the existing stability analysis approaches causes conservatism of their results in this paper to derive relaxed stability conditions for polynomial fmb control systems membership functions which are approximated with polynomials and carrying relations between membership functions and premise variables are brought into the stability analysis considering a polynomial fmb control system and based on the lyapunov stability theory stability conditions in the form of fuzzy summations are derived where each term contains product of membership functions of the polynomial fuzzy model and polynomial fuzzy controller each product term is approximated by a polynomial in order to obtain better approximation the operating domain of membership functions is partitioned to subregions then sos based stability conditions for all subregions are derived unlike some published stability analysis approaches the proposed one can be employed for stability analysis of polynomial fuzzy control systems under imperfect premise matching of which the fuzzy model and fuzzy controller do not share the same membership functions the solution of the sos based stability conditions can be found numerically using sostools which is a free third party matlab toolbox numerical examples are given to illustrate the effectiveness of the proposed stability conditions