partial actions and kms states on relative graph c algebras abstract the relative graph c algebras introduced by muhly and tomforde are generalizations of both graph algebras and their toeplitz extensions for an arbitrary graph e and a subset r of the set of regular vertices of e we show that the relative graph c algebra c e r is isomorphic to a partial crossed product for an action of the free group generated by the edge set on the relative boundary path space given a time evolution on c e r induced by a function on the edge set we characterize the kms states and ground states using an abstract result of exel and laca guided by their work on kms states for toeplitz cuntz krieger type algebras associated to infinite matrices we obtain complete descriptions of the convex sets of kms states of finite type and of kms states of infinite type whose associated measures are supported on recurrent infinite paths this allows us to give a complete concrete description of the convex set of all kms states for a big class of graphs which includes all graphs with finitely many vertices

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

dynamical systems associated to separated graphs graph algebras and paradoxical decompositions abstract we attach to each finite bipartite separated graph e c a partial dynamical system e c f where e c is a zero dimensional metrizable compact space f is a finitely generated free group and is a continuous partial action of f on e c the full crossed product c algebra o e c c e c f is shown to be a canonical quotient of the graph c algebra c e c of the separated graph e c similarly we prove that for any field k the algebraic crossed product l k ab e c c k e c alg f is a canonical quotient of the leavitt path algebra l k e c of e c the monoid v l k ab e c of isomorphism classes of finitely generated projective modules over l k ab e c is explicitly computed in terms of monoids associated to a canonical sequence of separated graphs using this we are able to construct an action of a finitely generated free group f on a zero dimensional metrizable compact space z such that the type semigroup s z f k is not almost unperforated where k denotes the algebra of clopen subsets of z finally we obtain a characterization of the separated graphs e c such that the canonical partial action of f on e c is topologically free

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

generalization of stability criterion for takagi sugeno continuous fuzzy model the stability analysis of a generalized class of continuous fuzzy systems in terms of lyapunov stability theory is presented firstly the stability problem of fuzzy systems described by takagi sugeno s continuous model is stated secondly new stability conditions which guarantee the stability of the fuzzy system are derived the new stability conditions can be regarded as a general solution for takagi sugeno fuzzy system in which the offset term is not equal to zero finally the suggested stability theorems are verified by some illustrative examples

harmonic analysis as spectral theory of laplacians by writing the fourier inversion formula on euclidean space in polar coordinates we obtain f x 0 fgl x dx where fgl x 2fgl x which is the spectral theory of the laplacian how do properties of f relate to properties of the family of eigenfunctions fgl answers are provided for the following spaces l2 s s d in odd dimensions analogous results are obtained for harmonic analysis on hyperbolic space constant curvature semi riemannian spaces the heisenberg group and for differential forms on hyperbolic space for f l2 there is a plancherel formula f 22 limt o 1t bt z f x 2dx d where bt z denotes the ball of radius t about an arbitrary point z which is independent of the dimension and the identical formula holds in hyperbolic space if the parametrization of the eigenvalues is shifted for certain semi riemannian symmetric spaces we obtain a paley wiener theorem that explains the role of discrete series in producing functions of compact support and also involve certain non unitary representations that contain the discrete series representations for the heisenberg group the plancherel formula is of a different nature requiring that the eigenfunctions be almost periodic in one variable

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

robust stabilization of the takagi sugeno fuzzy model via bilinear matrix inequalities quadratic stability has enabled mainly via the linear matrix inequality framework the analysis and design of a nonlinear control system from the local matrices of the system s takagi sugeno t s fuzzy model it is well known however that there exist stable differential inclusions hence t s fuzzy models whose stability is unprovable by a globally quadratic lyapunov function at present literature in the broader area of stability analysis suggests piecewise quadratic stability as a means to avoid such conservatism this paper generalizes the idea and proposes a framework that supports less conservative sufficient conditions for the stability of the t s model by using piecewise quadratic generalized lyapunov functions the advocated approach results in the formulation of the controller synthesis which herein aims for robust stabilization as a problem of bilinear rather than linear matrix inequalities simulation studies which include an algorithm for solution of bilinear matrix inequalities demonstrate the proposed method

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

model construction rule reduction and robust compensation for generalized form of takagi sugeno fuzzy systems this paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction rule reduction and robust compensation for nonlinear systems the model construction part replaces the nonlinear dynamics of a system with a generalized form of takagi sugeno fuzzy systems which is newly developed by us the generalized form has a decomposed structure for each element of a sub i and b sub i matrices in consequent parts the key feature of this structure is that it is suitable for constructing if then rules and reducing the number of if then rules the rule reduction part provides a successive procedure to reduce the number of if then rules furthermore we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models the robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties finally two examples demonstrate the utility of the systematic procedure developed

lp contractive projections and the heat semigroup for differential forms a projection operator that is contractive on lp for two distinct values of p is shown to be contractive for all values of p and the range must be of a special form this result is used to show that the heat semigroup for k forms on many manifolds with nontrivial cohomology in dimension k cannot be contractive on any lp for p 2

fuzzy rule based combination of linear and switching state feedback controllers this paper presents a fuzzy rule base combined controller which is a fuzzy rule based combination of linear and switching state feedback controllers for nonlinear systems subject to parameter uncertainties the switching state feedback controller is employed to drive the system states toward the origin when the system state approaches the origin the linear state feedback controller will gradually replace the switching state feedback controller the smooth transition between the linear and switching state feedback controllers is governed by the fuzzy rules by using the fuzzy rule based combination technique the proposed fuzzy rule base combined controller integrates the advantages of both the linear and switching state feedback controllers but eliminates their disadvantages as a result the proposed fuzzy controller provides good performance during the transient period and the chattering effect is removed when the system state approaches the origin stability conditions will be derived to guarantee the system stability furthermore a saturation function is employed to replace the switching component to alleviate the chattering during the transient period by using the proposed fuzzy rule based combination technique the steady state error introduced by the saturation function can be eliminated application examples will be given to show the merits of the proposed approach

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

the leavitt path algebra of a graph abstract for any row finite graph e and any field k we construct the leavitt path algebra l e having coefficients in k when k is the field of complex numbers then l e is the algebraic analog of the cuntz krieger algebra c e described in i raeburn graph algebras in cbms reg conf ser math vol 103 amer math soc 2005 the matrix rings m n k and the leavitt algebras l 1 n appear as algebras of the form l e for various graphs e in our main result we give necessary and sufficient conditions on e which imply that l e is simple

observer based robust h sub spl infin control for fuzzy systems using two step procedure this paper investigates both robust h sub spl infin analysis and synthesis problems involving observer based fuzzy control via linear matrix inequality methods for which efficient optimization techniques are available the observer and controller are capable of disturbance rejection in the presence of unknown but bounded disturbance we present results in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are demonstrated by examples

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

analysis and design of fuzzy control systems using dynamic fuzzy global models a method for analysis and design of a fuzzy controller is developed for a class of fuzzy discrete time systems the method is based on a dynamical fuzzy state space model it is shown that the closed loop fuzzy system can be represented by a dynamical interval system and thus the methods of stability analysis in uncertain linear system theory can be used to analyse the global stability of the closed loop fuzzy system some examples are given to illustrate the application of the method

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

stable controller design for t s fuzzy systems based on lie algebras in this paper we study the stability of fuzzy control systems of takagi sugeno t s type based on the classical theory of lie algebras t s fuzzy systems are used to model nonlinear systems as a set of rules with consequents of the type email protected t a lx t b lu t we conduct the stability analysis of such t s fuzzy models using the lie algebra l a generated by the a l matrices of these subsystems for each rule in the rule base we first develop our approach of stability analysis for a commuting algebra l a where all the consequent state matrices a l s commute we then generalize our results to the noncommuting case the basic idea here is to approximate the noncommuting lie algebra with a commuting one such that the approximation error is minimum the results of this approximation are extended to the most general case using the levi decomposition of lie algebras the theory is applied to the control of a flexible joint robot arm where we also present the decomposition procedure

a general fuzzy scheme for nonlinear processes with stability analysis abstract in this paper we develop a general fuzzy control scheme for nonlinear processes assuming little knowledge about the dynamics of the controlled process the proposed scheme starts by probing the process at different points in its operating region to generate a fuzzy quantisation a simple local controller is then designed at each fuzzy locality a fuzzy inference mechanism then links up tje local controllers to form a global controller which can be further refined by the learning algorithm by employing a newly developed structure adaptive fuzzy modelling scheme the appropriate fuzzy rule base for the inference mechanism can be extracted stably and efficiently the conditions for the stability of the global controller are rigourously established simulation results are presented to illustrate the effectiveness of the scheme

heat equation derivative formulas for vector bundles we use martingale methods to give bismut type derivative formulas for differentials and co differentials of heat semigroups on forms and more generally for sections of vector bundles the formulas are mainly in terms of weitzenbock curvature terms in most cases derivatives of the curvature are not involved in particular our results improve b k driver s formula in 1997 j math pures appl 9 76 703 737 for logarithmic derivatives of the heat kernel measure on a riemannian manifold our formulas also include the formulas of k d elworthy and x m li 1998 c r acad sci paris ser i math 327 87 92

existence of similarity transformation converting bmis to lmis under a mild condition we investigate the existence of a similarity transformation regarding robust hinfin stability analysis and observer controller synthesis problems the observer based controller is capable of disturbance rejection in the presence of unknown but bounded disturbance we present results which illustrate plainly the role of the similarity transformation in converting a bmi problem into an lmi problem in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are illuminated by examples

lpcontraction semigroups for vector valued functions abstract we discuss semigroups acting on vector valued functions we consider a comparison theorem between two semigroups a semigroup acting on scalar valued functions and a semigroup acting on vector valued functions the criterion is given by the abstract kato theorem by using this we give a sufficient condition for the criterion in the setting of square field operator we also consider the essential self adjointness of a perturbed semigroup

a groupoid approach to discrete inverse semigroup algebras abstract let k be a commutative ring with unit and s an inverse semigroup we show that the semigroup algebra ks can be described as a convolution algebra of functions on the universal etale groupoid associated to s by paterson this result is a simultaneous generalization of the author s earlier work on finite inverse semigroups and paterson s theorem for the universal c algebra it provides a convenient topological framework for understanding the structure of ks including the center and when it has a unit in this theory the role of gelfand duality is replaced by stone duality using this approach we construct the finite dimensional irreducible representations of an inverse semigroup over an arbitrary field as induced representations from associated groups generalizing the case of an inverse semigroup with finitely many idempotents more generally we describe the irreducible representations of an inverse semigroup s that can be induced from associated groups as precisely those satisfying a certain finiteness condition this finiteness condition is satisfied for instance by all representations of an inverse semigroup whose image contains a primitive idempotent

amenability for fell bundles given a fell bundle b over a discrete group we construct its reduced cross sectional algebra c r b in analogy with the reduced crossed products defined for c dynamical systems when the reduced and full cross sectional algebras of b are isomorphic we say that the bundle is amenable we then formulate an approximation property which we prove to be a sufficient condition for amenability a theory of graded c algebras possessing a conditional expectation is developed with an eye on the fell bundle that one naturally associates to the grading we show for instance that all such algebras are isomorphic to c r b when the bundle is amenable we also study induced ideals in graded c algebras and obtain a generalization of results of str til and voiculescu on af algebras and of nica on quasi lattice ordered groups a brief comment is made on the relevance to our theory of a certain open problem in the theory of exact c algebras an application is given to the case of an fn grading of the cuntz krieger algebras oa recently discovered by quigg and raeburn specifically we show that the cuntz krieger bundle satisfies the approximation property and hence is amenable for all matrices a with entries in 0 1 even if a does not satisfy the well known property i studied by cuntz and krieger in their paper

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

c algebras of separated graphs the construction of the c algebra associated to a directed graph e is extended to incorporate a family c consisting of partitions of the sets of edges emanating from the vertices of e these c algebras c e c are analyzed in terms of their ideal theory and k theory mainly in the case of partitions by finite sets the groups k0 c e c and k1 c e c are completely described via a map built from an adjacency matrix associated to e c one application determines the k theory of the c algebras um nnc confirming a conjecture of mcclanahan a reduced c algebra cred e c is also introduced and studied a key tool in its construction is the existence of canonical faithful conditional expectations from the c algebra of any row finite graph to the c subalgebra generated by its vertices differences between cred e c and c e c such as simplicity versus non simplicity are exhibited in various examples related to some algebras studied by mcclanahan

purely infinite simple reduced c algebras of one relator separated graphs abstract given a separated graph e c there are two different c algebras associated to it the full graph c algebra c e c and the reduced one c red e c for a large class of separated graphs e c we prove that c red e c either is purely infinite simple or admits a faithful tracial state the main tool we use to show pure infiniteness of reduced graph c algebras is a generalization to the amalgamated case of a result on purely infinite simple free products due to dykema

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

semiglobal stabilization of nonlinear systems using fuzzy control and singular perturbation methods singular perturbation methods based on a lyapunov approach are implemented for the derivation of sufficient conditions for the semiglobal stabilization with output tracking of nonlinear systems having internal dynamics the key idea of this approach lies in the decomposition of the full system into a subsystem exhibiting fast dynamics and to a subsystem with slow dynamics resulting in a substantial simplification of the stability analysis this two time scale behavior is achieved by implementing a properly designed fuzzy logic controller the key element of the proposed model based composite controller for the construction of the model based controller a new identification technique based on both classical and fuzzy tools is proposed results are presented for the semiglobal stabilization of a continuous stirred tank reactor which is a process with high nonlinear behavior

a methodology to design stable nonlinear fuzzy control systems the stability of nonlinear systems has to be investigated without making linear approaches in order to do this there are several techniques based on lyapunov s second method for example krasovskii s method allows to prove the sufficient condition for the asymptotic stability of nonlinear systems this method requires the calculation of the jacobian matrix in this paper an equivalent mathematical closed loop model of a multivariable nonlinear control system based on fuzzy logic theory is developed later this model is used to compute the jacobian matrix of a closed loop fuzzy system next an algorithm to solve the jacobian matrix is proposed the algorithm uses a methodology based on the extension of the state vector the developed algorithm is completely general it is independent of the type of membership function that is chosen for building the fuzzy plant and controller models and it allows the compound of different membership functions in a same model we have developed a matlab s function that implements the improved algorithm together with a series of additional applications for its use the designed software provides complementary functions to facilitate the reading and writing of fuzzy systems as well as an interface that makes possible the use of all the developed functions from the matlab s environment which allows to complement and to extend the possibilities of the matlab s fuzzy logic toolbox an example with a fuzzy controller for a nonlinear system to illustrate the design procedure is presented the work developed in this paper can be useful for the analysis and synthesis of fuzzy control systems

a new approach to fuzzy modeling and control of discrete time systems we present a new approach to fuzzy modeling and control of discrete time systems which is based on the formulation of a novel state space representation using the hyperbolic tangent function the new representation designated the hyperbolic model combines the advantages of fuzzy system theory and classical control theory on the one hand the hyperbolic model is easily derived from a set of mamdani type fuzzy rules on the other hand classical control theory can be applied to design controllers for the hyperbolic model that not only guarantee stability and robustness but are themselves equivalent to a set of mamdani type fuzzy rules thus this new approach combines the best of two worlds it enables linguistic interpretability of both the model and the controller and guarantees closed loop stability and robustness

convex subshifts separated bratteli diagrams and ideal structure of tame separated graph algebras abstract we introduce a new class of partial actions of free groups on totally disconnected compact hausdorff spaces which we call convex subshifts these serve as an abstract framework for the partial actions associated with finite separated graphs in much the same way as classical subshifts generalize the edge shift of a finite graph we define the notion of a finite type convex subshift and show that any such subshift is kakutani equivalent to the partial action associated with a finite bipartite separated graph we then study the ideal structure of both the full and the reduced tame graph c algebras o e c and o r e c of a separated graph e c and of the abelianized leavitt path algebra l k ab e c as well these algebras are the reduced crossed products with respect to the above mentioned partial actions and we prove that there is a lattice isomorphism between the lattice of induced ideals and the lattice of hereditary d saturated subsets of a certain infinite separated graph f d built from e c called the separated bratteli diagram of e c we finally use these tools to study simplicity and primeness of the tame separated graph algebras

graphical and numerical approach to robust stability analysis of fuzzy modeled systems with parametric uncertainty and disturbance abstract in this paper robust stability analysis methods for the fuzzy feedback control systems are presented the graphical method via multivariable circle criterion and the numerical method via linear matrix inequalities lmi the well known takagi sugeno fuzzy model is used as the nonlinear plant model uncertainties are assumed to be included in the model structure with known bounds for these structured parametric uncertainties l 2 robust stability analysis is performed by taking external disturbance as input and system state as output the effectiveness of the proposed methods is illustrated by examples

quadratic stability analysis of the takagi sugeno fuzzy model the nonlinear dynamic takagi sugeno fuzzy model with offset terms is analyzed as a perturbed linear system a sufficient criterion for the robust stability of this nominal system against nonlinear perturbations guarantees quadratic stability of the fuzzy model the criterion accepts a convex programming formulation of reduced computational cost compared to the common lyapunov matrix approach parametric robust control techniques suggest synthesis tools for stabilization of the fuzzy system application examples on fuzzy models of nonlinear plants advocate the efficiency of the method the examples demonstrate reduced conservatism compared to norm based criteria

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

stability issues on takagi sugeno fuzzy model parametric approach the main objective of this research is to provide a systematic stability analysis technique for fuzzy systems using well established results from robust stability of a family of polynomials the model based takagi sugeno 1985 fuzzy control system is considered and shown to have a dependent coefficient structure involving firing strengths two kharitonov regions via overbounding are established to facilitate the extreme results for stability test in the space of polynomials as well as the complex plane the criterion obtained is a sufficient condition for a fuzzy logic controller three nonlinear examples are demonstrated to show that the systematic approach proposed here can be used to solve fuzzy stability problems fuzzy users concerned over stability issues may find these analytic tools useful

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

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

stability analysis of control system having pd type of fuzzy controller stability of a control system having pd type of fuzzy controller a two input and single output controller is analyzed in this paper using yakubovich s method in this analysis the controller is treated as a two input and two output controller and the nonlinearity of the controller is characterized as the sector condition absolute stability conditions are derived for the control system as three conditions two are conditions for either one of control modes p or d is independently operating the third is the condition for two modes are simultaneously active the former two conditions are nothing but popov s conditions for two siso systems a new graphical method is proposed to solve the latter condition this method is explained illustratively using an example and the results obtained are compared numerically with those by other graphical methods as well as simulation results

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

robust h fuzzy static output feedback control of t s fuzzy systems with parametric uncertainties this paper addresses robust h fuzzy static output feedback control problem for t s fuzzy systems with time varying norm bounded uncertainties sufficient conditions for synthesis of a fuzzy static output feedback controller for t s fuzzy systems are derived in terms of a set of linear matrix inequalities lmis in comparison with the existing literatures the proposed approach not only simplifies the design procedure but also achieves a better h performance three drawbacks existing in the previous papers such as coordinate transformation same output matrices and bmi problem have been eliminated the effectiveness of the proposed design method is demonstrated by an example for the control of a truck trailer 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

an approach to the analysis of fuzzy systems this paper deals with a formal description of ill defined processes fuzzy systems by the use of fuzzy relational equations it is pointed out that fuzzy relational equations form a generalized version of the difference equations widely considered in control theory some equivalence between these two kinds of description is presented basic problems of fuzzy systems e g identification prediction sensitivity and stability are shown and numerical algorithms are given indices of each method are introduced especially the degree of fuzziness the sensitivity index which makes it possible to express the quality of each of them

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

fuzzy model based control of complex plants in the field of fuzzy modeling the takagi sugeno fuzzy model has been used to approximate accurately the dynamics of complex plants the paper addresses two control design problems associated with state space realizations of such fuzzy models first we treat the stability robustness of fuzzy model based controllers against modeling uncertainty second we develop observer based control schemes and further investigate the behavior of estimated state feedback in both cases we provide sufficient conditions that guarantee stability of the closed loop the results are demonstrated on the fuzzy model of a gas furnace process

lmi based design of stabilizing fuzzy controllers for nonlinear systems described by takagi sugeno fuzzy model abstract there have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controllers this paper reports on a related study of the takagi sugeno ts fuzzy systems and it is shown that the controller synthesis problems for the nonlinear systems described by the ts fuzzy model can be reduced to convex problems involving linear matrix inequalities lmis after classifying the ts fuzzy systems into three families based on how diverse their input matrices are a unique controller synthesis procedure is given for each of the families a numerical example is presented to illustrate the synthesis procedures developed in this paper

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

k theory for the tame c algebra of a separated graph abstract a separated graph is a pair e c consisting of a directed graph e and a set c v e 0 c v where each c v is a partition of the set of edges whose terminal vertex is v given a separated graph e c such that all the sets x c are finite the k theory of the graph c algebra c e c is known to be determined by the kernel and the cokernel of a certain map denoted by 1 c a e c from z c to z e 0 in this paper we compute the k theory of the tame graph c algebra o e c associated to e c which has been recently introduced by the authors letting denote the natural surjective homomorphism from c e c onto o e c we show that k 1 is a group isomorphism and that k 0 is a split monomorphism whose cokernel is a torsion free abelian group we also prove that this cokernel is a free abelian group when the graph e is finite and determine its generators in terms of a sequence of separated graphs e n c n n 1 naturally attached to e c on the way to showing our main results we obtain an explicit description of a connecting map arising in a six term exact sequence computing the k theory of an amalgamated free product and we also exhibit an explicit isomorphism between ker 1 c a e c and k 1 c e c

on lp contractivity of semigroups generated by linear partial differential operators abstract this paper is devoted to the study of contraction semigroups generated by linear partial differential operators it is shown that linear partial differential operators of order higher than two cannot generate contraction semigroups on l p n for p 1 unless p 2 if p 1 and the l p dissipativity criterion is restricted to the cone of nonnegative functions for differential operators with real valued coefficients it is proven that the criterion still fails for operators of order higher than two except for some fourth order operators if 3 2 p 3 a class of such fourth order operators is also presented

fuzzy modeling and control of multilayer incinerator abstract a method to design a fuzzy controller based on a fuzzy model is suggested the identification method of a fuzzy model is also discussed the suggested method is applied for the modelling and control of a multilayer incinerator the performance of the designed fuzzy controller is tested by computer simulation using the identified process model the results are satisfactory

control laws for takagi sugeno fuzzy models abstract this work presents control laws for fuzzy models of takagi sugeno ts sugeno and kang fuzzy sets and systems 28 1988 15 33 takagi and sugeno ieee trans systems man cybernet 15 1 1985 116 132 these laws are not directly put in the classical form called pdc for parallel distributed compensation wang et al ieee trans fuzzy systems 4 1 1996 14 23 on a particular family of ts fuzzy models the approach allows to reduce the conservatism of results found in the literature tanaka et al ieee trans fuzzy systems 6 2 1998 1 16 this approach utilizes the state space representation according to that remark observers are also considered and a separation principle is also given though results are provided mainly for the continuous case they are also provided for the discrete case an example in both cases illustrates the results obtained

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

enveloping actions and takai duality for partial actions we show that any partial action on a topological space x is the restriction of a suitable global action called enveloping action that is essentially unique in the case of c algebras we prove that any partial action has a unique enveloping action up to morita equivalence and that the corresponding reduced crossed products are morita equivalent the study of the enveloping action up to morita equivalence reveals the form that takai duality takes for partial actions by applying our constructions we prove that the reduced crossed product of the reduced cross sectional algebra of a fell bundle by the dual coaction is liminal postliminal or nuclear if and only if so is the unit fiber of the bundle we also give a non commutative generalization of the well known fact that the integral curves of a vector field on a compact manifold are defined on all of r

convergence property of interval matrices and interval polynomials in association with robust control system design and analysis the hurwitz property of interval matrices and interval polynomials has recently been actively investigated however its discrete counterpart the convergence property has seemingly not been much discussed in this paper this property is studied in comparison with the hurwitz counterpart some conditions under which interval matrices or interval polynomials are convergent are derived

identification of dynamic fuzzy models this paper discusses a new type of dynamic fuzzy model for the control of complex systems the fuzzy model has two maps one is a global rule map to describe the global approximation inference effects the other is the local rule map to describe the properties of the inference rule on the local area a simple example is given to show how the fuzzy model can be used to design a controller an identification method is described to identify the dynamic fuzzy model this includes the determination of the number of fuzzy rules the structure and parameters of the local rule maps and the estimation of the parameters in the membership functions

robust fuzzy logic control of mechanical systems an approach for the design of fuzzy control laws for tracking control of a large class of mechanical systems is proposed the approach employs the framework of lyapunov s stability theory to formulate a class of control laws that guarantee convergence of the tracking errors to within specification limits in presence of bounded parameter uncertainties and input disturbances the proposed control laws possess a large number of parameters and functional relationships to be chosen by the designer according to a methodology developed in the paper the large number of design degrees of freedom makes the approach suitable for fuzzy logic implementation a number of fuzzy implementations of the proposed control methodology are provided all implementations guarantee tracking error convergence to within prespecified performance limits an extensive simulation study using a model of a two degree of freedom robot manipulator was conducted fuzzy and non fuzzy implementations of the proposed methodology were compared to control laws designed using other design methods simulation study results indicate a superiority of the proposed control methodology compared to other approaches the study also demonstrates better performance of the fuzzy control implementation compared to its non fuzzy counterpart

h2 and h fuzzy filters with memory for takagi sugeno discrete time systems abstract this paper is concerned with the problem of h 2 and h fuzzy filter design for takagi sugeno t s discrete time systems the novelty of the proposed method in the context of t s fuzzy systems is the inclusion of an arbitrary number of past information states and measurements in the structure of the filter producing a t s fuzzy filter with memory linear matrix inequality relaxations based on multi polynomial fuzzy lyapunov functions are proposed for the filter design providing filters that attain lower bounds for the h 2 and h performance criteria when compared to other approaches available in the fuzzy literature that employ memoryless filters the advantages of the proposed approach are illustrated by numerical examples

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

fuzzy controllers as gain scheduling approximators abstract nonlinear systems can be linearized according to lyapunov s linearization method and then approximated by takagi sugeno ts fuzzy models the paper shows that the corresponding control strategy with ts controllers is closely related to traditional gain scheduling generally speaking gain scheduling deals with the connection of different linear controllers acting as a global nonlinear control law ts control defines a linear controller for each linearized region as well as smooth control transitions between those regions in this connection slowly varying operating conditions are assumed for the design of the linear controllers the lqr design method has been used which guarantees optimal control of a linearized system with respect to an integral criterion however since ts control is an approximation method solutions are bound to be suboptimal and stability is hence a concern the method is compared with a continuous change of control parameters based on the continuous on line lqr design for each point in state space additional control rule weights have been introduced to promote optimization the above method is illustrated by a simple one link manipulator arm

partial actions and subshifts given a finite alphabet and a not necessarily finite type subshift x x we introduce a partial action of the free group f f on a certain compactification x x of x which we call the spectral partial action the space x x has already appeared in many papers in the subject arising as the spectrum of a commutative c algebra usually denoted by dxdx a good understanding of dxdx is crucial for the study of c algebras related to subshifts and since the descriptions given of x x in the literature are often somewhat terse and obscure one of our main goals is to present a sensible model for it which allows for a detailed study of its structure as well as of the spectral partial action from various points of view including topological freeness and minimality we then apply our results to study certain c algebras associated to x introduced by matsumoto and carlsen thus the spectral partial action permits us to endow the carlsen matsumoto c algebra oxox with a partial crossed product structure we combine this with our characterization of the dynamical properties of the spectral partial action in order to treat the problem of simplicity of oxox considered earlier by several authors as a new advance we are able to give necessary and sufficient conditions for oxox to be simple without imposing any restriction on x and this is done in terms of transparent graphical properties of x as a by product of our partial action approach we easily recover some known facts on oxox putting them more in line with mainstream techniques used to treat similar c algebras