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

a differential operator for symmetric functions and the combinatorics of multiplying transpositions by means of irreducible characters for the symmetric group formulas have previously been given for the number of ways of writing permutations in a given conjugacy class as products of transpositions these formulas are alternating sums of binomial coefficients and powers of integers combinatorial proofs are obtained in this paper by analyzing the action of a partial differential operator for symmetric functions

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

on the homology of the hilbert scheme of points in the plane geir ellingsrud 1 and stein arild stromme 2 i matematisk institutt universitetet i oslo blindern n oslo 3 norway 2 matematisk institutt universitetet i bergen n 5014 bergen norway although several authors have been interested in the hilbert scheme hilba ip z parametrizing finite subschemes of length d in the projective plane i1 i2 f 1 f2 br among others not much is known about the topological properties of this space the picard group has been calculated i f2 and the homology groups of hilb3 ip 2 have been computed hi in this paper we give a precise description of the additive structure of the homology of hilba ip2 applying the results of birula bialynicki b1 b2 on the cellular decompositions de fined by a torus action to the natural action of a maximal torus of sl 3 on hilbe ipz a rather easy consequence of the fact that this action has finitely many fixpoints is that the cycle maps between the chow groups and the homology groups are isomorphisms in particular there is no odd homology and the homology groups are all free the main objective of this work is to compute their ranks the betti numbers of hilba ipz as a byproduct of our method we get similar results on the homology of the punctual hilbert scheme and of the hilbert scheme of points in the affine plane it seems natural to generalize our results to any toric smooth surface however we give the results only for the rational ruled surfaces if with an indication of the necessary changes in the proofs for simplicity we work over the field of complex numbers but with an appropriate interpretation of the word homology our results remain valid over any base field

design of a polynomial fuzzy observer controller with sampled output measurements for nonlinear systems considering unmeasurable premise variables in this paper we propose a polynomial fuzzy observer controller for nonlinear systems where the design is achieved through the stability analysis of polynomial fuzzy model based pfmb observer control system the polynomial fuzzy observer estimates the system states using estimated premise variables the estimated states are then employed by the polynomial fuzzy controller for the feedback control of nonlinear systems represented by the polynomial fuzzy model the system stability of the pfmb observer control system is analyzed based on the lyapunov stability theory although using estimated premise variables in polynomial fuzzy observer can handle a wider class of nonlinear systems it leads to a significant drawback that the stability conditions obtained are nonconvex matrix decoupling technique is employed to achieve convex stability conditions in the form of sum of squares we further extend the design and analysis to polynomial fuzzy observer controller using a sampled data technique for nonlinear systems where only sampled output measurements are available simulation examples are presented to demonstrate the feasibility and validity of the design and analysis results

two step stability analysis for general polynomial fuzzy model based control systems this paper investigates the stability of a polynomial fuzzy model based pfmb control system formed by a nonlinear plant represented by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop three cases of polynomial fuzzy controllers are proposed for the control process with the consideration of a matched mismatched number of rules and or premise membership functions which demonstrate different levels of controller complexity design flexibility and stability analysis results a general polynomial lyapunov function candidate is proposed to investigate the system stability unlike the published work there is no constraint on the polynomial lyapunov function candidate which is independent of the form of the polynomial fuzzy model thus it can be applied to a wider class of pfmb control systems and potentially produces more relaxed stability analysis results two step stability conditions in terms of sum of squares sos are obtained to numerically find a feasible solution to facilitate the stability analysis and relax the stability analysis result the boundary information of membership functions is taken into account in the stability analysis and incorporated into the sos based stability conditions simulation examples are given to illustrate the effectiveness of the proposed approach

stability analysis and control of discrete type 1 and type 2 tsk fuzzy systems part i stability analysis this paper introduces sufficient conditions for the exponential stability of type 1 and type 2 takagi sugeno kang tsk fuzzy systems a major advantage of the new conditions is that they do not require the existence of a common lyapunov function and are therefore applicable to systems with unstable consequents in addition our results include two classes of type 2 tsk systems with type 1 consequents for which no stability tests are available the use of the conditions in stability testing is demonstrated using simple numerical examples that include cases where methods that are based on a common lyapunov function fail the application of the stability test to develop new controller design methodologies is presented in a separate paper i e part ii

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

robust static output feedback h control for uncertain fuzzy systems this paper will focus on robust static output feedback sof h control for discrete time takagi sugeno t s fuzzy systems with time varying norm bounded uncertainties first a new h performance analysis criterion is proposed for the fuzzy systems then sufficient conditions for designing fuzzy sof h controllers are given in terms of solutions to a set of linear matrix inequalities lmis in contrast to the existing methods for designing the sof h controllers the output matrices of the considered fuzzy system are allowed to be non common and to have uncertainties moreover theoretical proof is given to show that the proposed design conditions include some existing results as special cases simulation examples are provided to show the effectiveness of the proposed design method

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

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

output feedback control for t s fuzzy delta operator systems with time varying delays via an input output approach in this paper the problem of induced l 2 disturbance attenuation control is investigated for discrete time takagi sugeno t s fuzzy delta operator systems with time varying delays and disturbance input via an input output approach a model transformation method is utilized to approximate the time varying delay in t s fuzzy delta operator systems by applying the scaled small gain ssg theorem and lyapunov krasovskii functional approach a sufficient condition is established to guarantee that the closed loop system is asymptotically stable and has an induced l 2 disturbance attenuation performance the existence condition of the dynamic output feedback controller can be solved via convex optimization problems finally simulation results are given to demonstrate the feasibility and effectiveness of the proposed method

symmetric groups and the cup product on the cohomology of hilbert schemes let c sn be the z module of integer valued class functions on the symmetric group sn we introduce a graded version of the con volution product on c sn and show that there is a degree preserving ring isomorphism c sn h hilb n a 2 z to the cohomology of the hilbert scheme of points in the complex affine plane

te scattering by arbitrarily connected conducting strips the scattering by an arbitrary collection of perfectly conducting connected strips is analyzed for te incidence the studied configurations include both closed and open polygonal cross section cylinders as well as more complicated structures in which more than two strips are connected at a point the proposed method is very efficient as few expansion functions are needed in a galerkin scheme this is achieved by means of expansion functions factorizing the correct edge singularity of the electromagnetic field and ensuring the continuity of the current at connecting points

heisenberg algebra and hilbert schemes of points on projective surfaces the purpose of this paper is to throw a bridge between two seemingly unrelated subjects one is the hilbert scheme of points on projective surfaces which has been intensively studied by various people see e g i br es g61 g62 the other is the infinite dimensional heisenberg algebra which is closely related to affine lie algebras see e g k we shall construct a representation of the heisenberg algebra on the homology group of the hilbert scheme in other words the homology group will become a fock space the basic idea is to introduce certain correspondences in the product of the hilbert scheme then they define operators on the homology group by a well known procedure they give generators of the heisenberg algebra and the only thing we must check is that they satisfy the defining relation here we remark that the components of the hilbert scheme are parameterized by numbers of points and our representation will be constructed on the direct sum of homology groups of all components our correspondences live in the product of the different components thus it is quite essential to study all components together our construction has the same spirit as the author s construction nal na4 of representations of affine lie algebras on homology groups of moduli spaces of instantons 1 on ale spaces which are minimal resolutions of simple singularities certain correspondences called hecke correspondences were used to define operators these twist instantons along curves irreducible components of the exceptional set while ours twist ideals around points in fact the hilbert scheme of points can be considered as the moduli space of rank 1 vector bundles or more precisely torsion free sheaves our construction should be considered as a first step to extend nal na4 to general 4 manifolds the same program was also proposed by ginzburg kapranov and vasserot gkv

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

adaptive synchronization of uncertain chaotic systems based on t s fuzzy model this paper presents an adaptive approach for synchronization of takagi sugeno t s fuzzy chaotic systems t s fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive system since the output of the drive system is only available for synchronization the response system is designed based on fuzzy adaptive observer for uncertain parameters and parameter mismatch cases we analyze the stability of the overall fuzzy synchronization system by applying lyapunov stability theory and derive stability conditions by solving linear matrix inequalities lmis problem the adaptive law is derived to estimate the uncertain parameters or parameter mismatch numerical examples are given to demonstrate the validity of the proposed fuzzy adaptive synchronization approach

state feedback control of continuous time t s fuzzy systems via switched fuzzy controllers this paper studies the problem of state feedback control of continuous time t s fuzzy systems switched fuzzy controllers are exploited in the control design which are switched based on the values of membership functions and the control scheme is an extension of the parallel distributed compensation pdc scheme sufficient conditions for designing switched state feedback controllers are obtained with meeting an h norm bound requirement and quadratic d stability constraints it is shown that the new control design method provides less conservative results than the corresponding ones via the parallel distributed compensation pdc scheme a numerical example is given to illustrate the effectiveness of the proposed method

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

stability analysis of polynomial fuzzy model based control systems with mismatched premise membership functions this paper investigates the stability of polynomial fuzzy model based pfmb control system which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop to enhance the design flexibility the number of rules and the shape of premise membership functions of the polynomial fuzzy controller are considered to be chosen freely and are different from those of the polynomial fuzzy model however which make the stability analysis more difficult and potentially lead to conservative stability analysis result a sum of squares sos based stability analysis approach using the lyapunov stability theory is proposed to investigate the stability of the pfmb control systems and synthesize the polynomial fuzzy controller to facilitate the stability analysis and relax the stability analysis result the property of the membership functions and the boundary information of the membership grades and premise variables are taken into account in the stability analysis and incorporated into the sos based stability conditions a simulation example is given to illustrate the effectiveness of the proposed approach

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

flexible stability criteria for a linguistic fuzzy dynamic system abstract this paper considers the stability problems of continuous and discrete type fuzzy control systems respectively on the basis of matrix measures and matrix norms several stability criteria for the systems are proposed some of these criteria are flexible with different chosen parameter p that means the trade off between the conservativeness and the computing convenience of the criteria depends on the chosen value of p totally

polynomial fuzzy model based control systems stability analysis via piecewise linear membership functions this paper presents the stability analysis of polynomial fuzzy model based pfmb control systems using the sum of squares sos approach the pfmb control system under consideration requires that the polynomial fuzzy model and polynomial fuzzy controller share neither the same premise membership functions nor the same number of fuzzy rules this class of pfmb control systems offers a greater design flexibility to the polynomial fuzzy controller however due to the imperfectly matched membership functions it usually produces more conservative stability conditions by following the traditional stability analysis approach for the fmb control systems to facilitate the stability analysis piecewise linear membership functions plmfs are proposed which offer a nice property that the grades of membership are governed by a finite number of sample points thus it allows the plmfs to be brought to the sos based stability conditions which are applied to the pfmb control systems with the specified plmfs rather than any shapes the system stability can be examined by checking only the pfmb control system at the sample points it is worth mentioning that the plmfs which are not necessarily implemented physically are a mathematical tool to carry out the stability analysis to verify the stability analysis result a simulation example is given to demonstrate the effectiveness of the proposed approach

relaxed stability and performance lmi conditions for takagi sugeno fuzzy systems with polynomial constraints on membership function shapes most linear matrix inequality lmi fuzzy control results in literature are valid for any membership function i e independent of the actual membership shape hence they are conservative with respect to other nonlinear control approaches when specific knowledge of the shapes is available this paper presents relaxed lmi conditions for fuzzy control that incorporate such shape information in the form of polynomial constraints generalizing previous works by the authors interesting particular cases are overlap product bounds and ellipsoidal regions numerical examples illustrate the achieved improvements as well as the possibilities of solving some multiobjective problems the results also apply to polynomial in membership takagi sugeno fuzzy systems

lmi based fuzzy chaotic synchronization and communications addresses synthesis approaches for signal synchronization and secure communications of chaotic systems by using fuzzy system design methods based on linear matrix inequalities lmis by introducing a fuzzy modeling methodology many well known continuous and discrete chaotic systems can be exactly represented by takagi sugeno t s fuzzy models with only one premise variable following the general form of fuzzy chaotic models the structure of the response system is first proposed then according to the applications of synchronization to the fuzzy models that have common bias terms or the same premise variable of drive and response systems the driving signals are developed with four different types fuzzy character crisp and predictive driving signals synthesizing from the observer and controller points of view all types of drive response systems achieve asymptotic synchronization for chaotic communications the asymptotical recovering of messages is ensured by the same framework it is found that many well known chaotic systems can achieve their applications on asymptotical synchronization and recovering messages in secure communication by using either one type of driving signals or all several numerical simulations are shown with expected satisfactory performance

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

a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems this paper proposes a new quadratic stabilization condition for takagi sugeno t s fuzzy control systems the condition is represented in the form of linear matrix inequalities lmis and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature a rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases in comparison with conventional conditions the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design the latter design work is quite hard for t s fuzzy control systems based on the lmi based conditions derived one can easily synthesize controllers for stabilizing t s fuzzy control systems since only a set of lmis is involved the controller design is quite simple and numerically tractable finally the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous time nonlinear system

more relaxed stability analysis and positivity analysis for positive polynomial fuzzy systems via membership functions dependent method abstract in this paper the conservatism source of the positivity and stability analysis results of positive polynomial fuzzy model based ppfmb control system are studied also in order to improve the flexibility of controller design a fuzzy controller that does not depend on the membership functions of the fuzzy model is designed in the existing literatures it is proved that the lclf can reduce the conservatism of stability results however the lclf generally results in non convex conditions which is still a conservatism source to handle the non convex conditions the sector nonlinear concept is applied to handle non convex terms in stability conditions and the obstacles caused by mismatched membership functions can be eliminated by plmf dependent method in addition to relax the conservatism caused by the lack of membership functions information the plmf dependent positivity analysis are performed for the first time meanwhile plmf dependent method is extended to stability conditions to obtained more relaxed conditions finally a simulation example is presented to verify the feasibility of this method

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

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

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

approaches to quadratic stability conditions and h sub spl infin control designs for t s fuzzy systems in this paper the problems of quadratic stability conditions and h sub spl infin control designs for takagi sugeno t s fuzzy systems have been studied first a new quadratic stability condition which is more simple than that in a previous paper has been proposed second two new sufficient conditions in the terms of linear matrix inequalities lmis which guarantee the existence of the state feedback h sub spl infin control for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally based on the lmis the h sub spl infin controller designing methods for the t s fuzzy systems have been given

vertex algebras and the cohomology ring structure of hilbert schemes of points on surfaces using vertex algebra techniques we determine a set of generators for the cohomology ring of the hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers

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

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

analytical structure and characteristics of symmetric karnik mendel type reduced interval type 2 fuzzy pi and pd controllers this paper presents the analytical structure of a class of interval type 2 it2 fuzzy proportional derivative pd and proportional integral pi controllers that have symmetrical rule base and symmetrical consequent sets two assumptions are made 1 the zadeh and operator is employed as the t norm operator 2 type reduction is performed by the karnik mendel km type reduction method the main contributions are the methodology that identifies the input conditions where the km algorithm uses a new switch point to compute the bounds of the type reduced set the closed form expressions that relate the inputs and output of an it2 fuzzy controller and insights into the potential performance improvement because of the inclusion of the footprint of uncertainty fou compared with its t1 counterpart two additional fou parameters generate 31 extra local regions each providing a unique relationship between the inputs and output signals the generation of a relatively large number of local regions at the cost of two extra design parameters indicates that an it2 fuzzy controller may be able to provide better performance furthermore by comparing the analytical structure with the corresponding t1 counterpart the potential advantages to use the it2 over the t1 fuzzy controller are studied four interesting characteristics are identified and they provide insights into why the it2 fuzzy controller may better balance the conflicting aims of fast rise time and small overshoot

exact output regulation for nonlinear systems described by takagi sugeno fuzzy models the exact output regulation for takagi sugeno t s fuzzy models depends on two conditions 1 the local steady state zero error manifolds have to be the same for every local subsystem and 2 the local input matrices have to be the same for every local subsystem included in the t s fuzzy model these conditions are difficult to satisfy in general in this paper those conditions are relaxed by solving the fuzzy regulation problem directly on the overall t s fuzzy model instead of constructing the fuzzy regulator on the basis of linear local controllers by considering the fuzzy model as a special class of linear time varying systems existence conditions are rigorously derived these new conditions which can be solved by means of any mathematical software depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and or the exosystem two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

stability analysis and systematic design of takagi sugeno fuzzy control systems abstract the stability analysis and systematic design techniques of takagi sugeno t s fuzzy control systems are discussed in this paper in order to make good use of the structural information in rule base to decrease the conservatism of the stability analysis the standard fuzzy partition of the input variables of fuzzy control systems is well defined based on the property analysis of fuzzy control systems with sfp inputs the stability of both the input free t s fuzzy systems and the closed loop t s fuzzy control systems are studied in detail with the extended lyapunov theory and two theorems to check the stability of t s fuzzy control systems are proposed these methods which only require to find a common positive definite symmetric matrix in each maximal overlapped rules group can reduce the conservatism and difficulty of the former stability analysis approaches using the method of parallel distributed compensation a systematic design approach of t s fuzzy control systems is presented the simulation results of three examples show that these methods are effective

a novel control design on discrete time takagi sugeno fuzzy systems with time varying delays this paper focuses on analyzing a new model transformation of discrete time takagi sugeno t s fuzzy systems with time varying delays and applying it to dynamic output feedback dof controller design a new comparison model is proposed by employing a new approximation for time varying delay state and then a delay partitioning method is used to analyze the scaled small gain of this comparison model a sufficient condition on discrete time t s fuzzy systems with time varying delays which guarantees the corresponding closed loop system to be asymptotically stable and has an induced l2 disturbance attenuation performance is derived by employing the scaled small gain theorem then the solvability condition for the induced l2 dof control is also established by which the dof controller can be solved as linear matrix inequality optimization problems finally examples are provided to illustrate the effectiveness of the proposed approaches

brief paper adaptive sliding mode controller design based on t s fuzzy system models an adaptive sliding mode control asmc technique based on t s fuzzy system models is proposed in this paper for a class of perturbed nonlinear mimo dynamic systems in order to solve tracking problems a t s fuzzy model is firstly formed by utilizing fuzzy theorem to amalgamate a set of linearized dynamic equations the adaptive sliding mode controller is then designed based on this fuzzy model with perturbations the proposed control scheme can drive the dynamics of controlled system into a designated sliding surface in finite time and guarantee the property of asymptotical stability it is also shown that the information of upper bound of modeling errors as well as perturbations except the information of upper bound of input uncertainty is not required when using the proposed controller

virasoro algebra and wreath product convolution abstract we present a group theoretic construction of the virasoro algebra in the framework of wreath products this can be regarded as a counterpart of a geometric construction of lehn in the theory of hubert schemes of points on a surface

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

membership function dependent stability analysis of fuzzy model based control systems using fuzzy lyapunov functions this paper investigates the stability of fuzzy model based fmb control system formed by a t s fuzzy model and a fuzzy controller connected in a close loop based on a fuzzy lyapunov function a general fmb control system that the t s fuzzy model and fuzzy controller not sharing the same premise membership functions and or the same number of fuzzy rules is considered a membership function dependent stability analysis approach is proposed to consider the membership functions of both the t s fuzzy model and fuzzy controller in the stability analysis and incorporate them in the stability conditions in the form of linear matrix inequalities as the stability conditions are membership function dependent they are dedicated to the fmb control system with the specified membership functions under consideration it is thus the membership function dependent stability conditions are more relaxed compared to the existing membership function independent stability conditions a fuzzy lyapunov function is a weighted sum of quadratic functions which are required to be positive definite in most of the existing work in this paper this criterion is not required and thus the stability conditions can be further relaxed some simulation examples are given to demonstrate the merits of the proposed approach

a global exponential fuzzy observer design for time delay takagi sugeno uncertain discrete fuzzy bilinear systems with disturbance a robust h fuzzy observer is proposed for a class of time delay takagi sugeno t s uncertain discrete fuzzy bilinear systems with disturbance utilizing the lipschitz conditions and some variable transformations a linear matrix inequality lmi approach is developed and a sufficient condition is obtained to design the robust h fuzzy observer the robust h fuzzy observer for time delay t s uncertain discrete fuzzy bilinear systems with disturbance can be obtained directly through the lmis with no preassigned matrices the convergent rate of the error state can be estimated from the initial conditions and the delay time of t s uncertain discrete fuzzy bilinear systems the designed robust h fuzzy observer can guarantee the dynamics of the observer error to be globally exponentially stable and has a prescribed h performance a numerical example is given to demonstrate the feasibility and effectiveness of the proposed observer design method

the cup product of hilbert schemes for k3 surfaces to any graded frobenius algebra a we associate a sequence of graded frobenius algebras a n so that there is canonical isomorphism of rings h x 2 n h x n 2n for the hilbert scheme x n of generalised n tuples of any smooth projective surface x with numerically trivial canonical bundle

lmi based integral fuzzy control of dc dc converters in this paper we propose a t s fuzzy controller which combines the merits of i the capability for dealing with nonlinear systems ii the powerful lmi approach to obtain control gains iii the high performance of integral controllers iv the workable rigorous proof for exponential convergence of error signals and v the flexibility on tuning decay rate the output regulation problems of a basic buck converter and a zero voltage transition zvt buck converter are used as application examples to illustrate the control performance of the proposed methodology first we consider a general nonlinear system which can represent the large signal models of the converters after introducing an added integral state of output regulation error and taking coordinate translation on an equilibrium point the resulting augmented system is represented into a takagi sugeno t s fuzzy model then the concept of parallel distributed compensation is applied to design the control law whereby the control gains are obtained by solving linear matrix inequalities lmis an interesting result is that the obtained control law is formed only by the linear state feedback signals weighted by grade functions in addition the robustness analysis is carried out when uncertainty and disturbance are taken into consideration the performance of numerical simulations and practical experiments results is satisfactory

design of polynomial fuzzy observer controller with membership functions using unmeasurable premise variables for nonlinear systems in this paper the stability of polynomial fuzzy model based pfmb observer control system is investigated via lyapunov stability theory the polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states then the estimated system states are used for the state feedback control of nonlinear systems although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the fuzzy model based fmb control strategy it leads to non convex stability conditions therefore the refined completing square approach is proposed to derive convex stability conditions in the form of sum of squares sos with less manually designed parameters in addition the membership functions of the polynomial observer controller are optimized by the improved gradient descent method which outperforms the widely applied parallel distributed compensation pdc approach according to a general performance index simulation examples are provided to verify the proposed design and optimization scheme

an intersection number for the punctual hilbert scheme of a surface we compute the intersection number between two cycles a and b of complementary dimensions in the hilbert scheme h parameterizingr subschemes of given finite length n of a smooth projective surface s the n 1 cycle a corresponds to the set of finite closed subschemes the support of which has cardinality 1 the n 1 cycle b consists of the closed subschemes the support of which is one given point of the surface since b is contained in a indirect methods are needed the intersection number is a b 1 n 1n answering a question by h nakajima

polynomial fuzzy model based control systems stability analysis via approximated membership functions considering sector nonlinearity of control input this paper presents the stability analysis of polynomial fuzzy model based pfmb control systems in which both the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions in order to address the input nonlinearity the control signal is considered to be bounded by a sector with nonlinear bounds these nonlinear lower and upper bounds of the sector are constructed by combining local bounds using fuzzy blending such that local information of input nonlinearity can be taken into account with the consideration of imperfectly matched membership functions and input nonlinearity the applicability of the pfmb control scheme can be further enhanced to facilitate the stability analysis a general form of approximated membership functions representing the original ones is introduced as a result approximated membership functions can be brought into the stability analysis leading to relaxed stability conditions the sum of squares approach is employed to obtain the stability conditions based on lyapunov stability theory simulation examples are presented to demonstrate the feasibility of the proposed method

membership dependent stability conditions for type 1 and interval type 2 t s fuzzy systems abstract this paper presents an idea to simplify and relax the stability conditions of takagi sugeno t s fuzzy systems based on the membership function extrema 1 by considering the distribution of membership functions in a unified membership space a graphical approach is provided to analyze the conservativeness of membership dependent stability conditions membership function extrema are used to construct a simple and tighter convex polyhedron that encloses the membership trajectory and produces less conservative linear matrix inequality lmi conditions the cases of both type 1 and interval type 2 t s fuzzy systems are considered and comparison with existing methods is made in the proposed membership vector framework

nonquadratic stabilization of continuous t s fuzzy models lmi solution for a local approach this paper is concerned with nonquadratic stabilization design problem for continuous time nonlinear models in the takagi sugeno t s form obtained by sector nonlinearity approach most of the previous results found in the literature intended to establish global nonquadratic stabilization conditions which are hard to uphold due to the difficulty of handling time derivatives of the membership function by changing the paradigm of global stabilization for something less restrictive a local solution to overcome infeasible quadratic stabilization conditions is offered in this paper it is shown that the derived local nonquadratic conditions actually lead to reasonable advantages over the existing quadratic approach as well as some previous nonquadratic attempts moreover conditions for the solvability of state feedback controller design given here are written in the form of linear matrix inequalities lmis which can be efficiently solved by convex optimization techniques simulation examples are given to demonstrate the validity and applicability of the proposed approaches

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

further theoretical justification of the k samples variation approach for discrete time takagi sugeno fuzzy systems the recently developed k samples variation approach is known as a powerful way to reduce the conservativeness of existing stability and stabilization conditions for discrete time takagi sugeno t s fuzzy systems in this approach the lyapunov functions under consideration are not necessarily decreasing at every sample but are allowed to decrease every k samples which is evidently less restrictive than classical approaches consequently less conservative linear matrix inequality lmi conditions were derived in addition it was proved that for two positive integers k1 and k2 if the condition for k k1 is fulfilled then those corresponding to k k2 are also satisfied when k2 is the divisor of k1 in this letter we prove that if the condition for k k2 admits a solution then those corresponding to any k k2 are also solvable