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

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

series expansion for a stochastic sandpile using operator algebra we extend the series for the activity density in a one dimensional stochastic sandpile with fixed particle density p the first terms of which were obtained via perturbation theory dickman and vidigal 2002 j phys a math gen 35 7269 the expansion is in powers of the time the coefficients are polynomials in p we devise an algorithm for evaluating expectations of operator products and extend the series to constructing pade approximants to a suitably transformed series we obtain predictions for the activity that compare well against simulations in the supercritical regime

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

adaptive fuzzy identification and control for a class of nonlinear pure feedback mimo systems with unknown dead zones the adaptive fuzzy identification and control problems are considered for a class of multi input multi output nonlinear systems with unknown functions and unknown dead zone inputs the main characteristics of the considered systems are that 1 they are composed of n subsystems and each subsystem is in nested lower triangular form 2 dead zone inputs are in nonsymmetric nonlinear form and 3 dead zone inputs appear nonlinearly in the systems and their parameters are not required to be known the controller design for this class of systems is a difficult and complicated task because of the existences of unknown functions the couplings among the nested subsystems and the dead zone inputs in the controller design the fuzzy logic systems are employed to approximate the unknown functions and the differential mean value theorem is used to separate dead zone inputs to compensate for dead zone inputs the compensative terms are designed in the controllers the stability of the closed loop system is proved via the lyapunov stability theorem a simulation example is provided to validate the feasibility of the approach

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

an improved input delay approach to stabilization of fuzzy systems under variable sampling in this paper we investigate the problem of stabilization for sampled data fuzzy systems under variable sampling a novel lyapunov krasovskii functional lkf is defined to capture the characteristic of sampled data systems and an improved input delay approach is proposed by the use of an appropriate enlargement scheme new stability and stabilization criteria are obtained in terms of linear matrix inequalities lmis compared with the existing results the newly obtained ones contain less conservatism some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

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

graded witt kernels of the compositum of multiquadratic extensions with the function fields of pfister forms abstract let f be a field of characteristic 2 and w q f be the witt group of nonsingular quadratic forms over f let be a bilinear pfister form over f and l be a multiquadratic extension of f of separability degree less than of equal to 2 in this paper we compute the kernel of the natural homomorphism h 2 m 1 f h 2 m 1 l where h 2 m 1 f is the cokernel of the artin schreier operator f m f m d f m 1 given by x d x 1 x 1 d x m x m x 2 x d x 1 x 1 d x m x m where f m is the space of m differential forms over f and f is the function field of the affine quadric given by the diagonal quadratic form associated to the bilinear form as a consequence we deduce the kernel of the natural homomorphisms i q m 1 f i q m 1 l and i q m 1 f i q m 1 l where i q m 1 f denotes the quotient i q m 1 f i q m 2 f such that i q m 1 f i m f w q f and i m f is the m th power of the fundamental ideal if of the witt ring of f bilinear forms we also include some results concerning the case where is replaced by a bilinear pfister neighbor or a quadratic pfister form

event based reliable dissipative filtering for t s fuzzy systems with asynchronous constraints in this paper event triggered reliable dissipative filtering is investigated for a class of takagi sugeno t s fuzzy systems first a reliable event triggered communication scheme is introduced to release sampled measurement outputs only if the variation of the sampled vector exceeds a prescribed threshold condition second an asynchronous premise reconstruct method for t s fuzzy systems is presented which relaxes the assumption of the prior work that the premises of the plant and the filter are synchronous third the resulting filtering error system is modeled under consideration of event triggered communication sensor failure and asynchronous premise in a unified framework by adopting the lyapunov functional method and integral inequality approach a delay dependent criterion is developed to guarantee asymptotic stability for the filtering error systems and achieve strict q s r alpha dissipativity consequently suitable filters and the event parameters can be derived by solving a set of linear matrix inequalities finally an example is given to show the effectiveness of the proposed method

universality classes in directed sandpile models we perform large scale numerical simulations of a directed version of the two state stochastic sandpile model numerical results show that this stochastic model defines a new universality class with respect to the abelian directed sandpile the physical origin of the different critical behaviour has to be ascribed to the presence of multiple topplings in the stochastic model these results provide new insight into the long debated question of universality in abelian and stochastic sandpiles

on some invariants of fields of characteristic p 0 abstract let k be a field of characteristic p 0 k n the k vector space of n differential forms and k n k n d k n 1 the artin schreier operator given by x d x 1 x 1 d x n x n x p x d x 1 x 1 d x n x n let h p n 1 k coker and define p k min m h p m 1 k 0 we show that for any finite extension l k p k p l p k 1

fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems this paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations pdes both distributed measurement form and collocated boundary measurement form are considered a takagi sugeno t s fuzzy pde model is first applied to accurately represent the semilinear parabolic pde system based on the t s fuzzy pde model two types of fuzzy boundary controllers which are easily implemented since only boundary actuators are used are proposed to ensure the exponential stability of the resulting closed loop system sufficient conditions of exponential stabilization are established by employing the lyapunov direct method and the vector valued wirtinger s inequality and presented in terms of standard linear matrix inequalities finally the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples

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

fuzzy dynamic output feedback control through nonlinear takagi sugeno models we present a convex way to design a fuzzy dynamic output feedback compensator for locally stabilizing a class of nonlinear discrete time systems this class consists of the systems described by takagi sugeno t s models with a sector bounded nonlinear additive term and saturated control signals the local stabilization takes into account the domain of validity of these t s models which is a key issue for practical applications two types of nonlinear fuzzy compensators are considered one having all matrices of the controller depending on fuzzy grade membership functions and the other with only a subset of the matrices with such a dependency the controller design includes a fuzzy anti windup gain that handles saturating actuators besides a time performance index based on the contractivity of the level set of the fuzzy lyapunov function is proposed regarding the closed loop system examples are given to illustrate the effectiveness of this proposal

network based h control for t s fuzzy systems with an adaptive event triggered communication scheme abstract this paper extends the prior work of discrete event triggered communication for networked t s fuzzy systems where the next communication instant is determined by an event triggered communication scheme with a constant threshold and the premises of t s fuzzy systems and parallel distribution compensation pdc fuzzy control rules are synchronous firstly an adaptive event triggered communication scheme for ncss is presented which relaxes the assumption of the prior work that the threshold of event triggered communication scheme is a preselected constant secondly an asynchronous premise re construct method for networked t s fuzzy systems is proposed which relaxes the assumption of the prior work that the premises of the plant and the pdc control rules are synchronous we show that the number of transmitted packets generated by the proposed scheme is smaller than those generated by some existing ones while ensuring the desired control performance simulations show 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

steady state of stochastic sandpile models we study the steady state of the abelian sandpile models with stochastic toppling rules the particle addition operators commute with each other but in general these operators need not be diagonalizable we use their abelian algebra to determine their eigenvalues and the jordan block structure these are then used to determine the probability of different configurations in the steady state we illustrate this procedure by explicitly determining the numerically exact steady state for a one dimensional example for systems of size 12 and also study the density profile in the steady state

multiobjective investment policy for a nonlinear stochastic financial system a fuzzy approach the financial market always suffers from continuous and discontinuous jump changes and can be regarded as a nonlinear stochastic jump diffusion system most investors expect their investment policies to be not only higher benefits but also lower risk as a multiobjective optimization problem mop in this study a multiobjective h 2 h infty fuzzy investment is proposed for nonlinear stochastic jump diffusion financial systems to achieve the desired target with minimum investment cost and risk in pareto optimal sense simultaneously the takagi sugeno t s fuzzy model is used to approximate the nonlinear stochastic jump diffusion financial system to simplify the multiobjective h 2 h infty investment policy design procedure by the help of the t s fuzzy model the multiobjective h 2 h infty fuzzy investment policy problem of nonlinear stochastic financial system can be transformed to a linear matrix inequality constrained lmi constrained mop to avoid solving the annoying hamilton jacobi inequalities because the lmi constrained mop is not easy to directly calculate its pareto optimal solutions an indirect method is proposed to solve this mop for the multiobjective h 2 h infty fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems an lmi constrained multiobjective evolution algorithm lmi constrained moea is also developed to efficiently solve the pareto optimal solutions of the lmi constrained mop for the multiobjective h 2 h infty fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems when the pareto optimal regulation solutions are solved by the proposed lmi constrained moea investors can select one investment policy to achieve their desired target with minimum investment cost and risk according to his her own preference

symmetric bilinear forms quadratic forms and milnor k theory in characteristic two is bijective for any field f of characteristic two and for any n 0 here k f is the k group of milnor defined in 11 and i is the unique maximal ideal of the witt ring w f of non degenerate symmetric bilinear forms over f on the other hand sah studied quadratic forms in characteristic two in 15 let f be a field of characteristic two wq f the witt group of non degenerate quadratic forms over f and define i wq f n o by the canonical w f module structure on wq f then he proved that wq f iwq f is isomorphic to the group of quadratic cyclic extensions of f and iwq f i2wq f is isomorphic to the subgroup br f 2 of the brauer group br f of f consisting of elements annihilated by 2 in this paper we prove the above milnor s conjecture and describe the precise structures of w f and wq f generalizing the result of sah for any field f of characteristic p 0 let be the n th exterior power over f of the absolute differential module n t g21 let d 2 1 be the f z f fp image of the exterior derivation d f2 t f2 and let v n v resp h 1 f be the kernel resp cokernel of the homomorphism

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

novel stabilization criteria for t s fuzzy systems with affine matched membership functions this paper presents a new parallel distributed compensation controller design approach for t s takagi sugeno fuzzy control systems with affine matched membership functions in the system and controller in the new fuzzy control affine transformed membership functions are adopted by scaling and biasing the original membership functions of the system stabilization and performance criterion of the closed loop t s fuzzy systems are obtained through a new parameterized linear matrix inequality which is rearranged by affine matched membership functions the conservativeness of stabilization condition for the t s fuzzy system is significantly relaxed by utilizing the constraints condition of the controllers membership functions which is determined from the difference of each transformed membership function in addition the controller gain is reconstructed by a decision variable separation technique with two different free weighting matrices without any scaling parameter the superiority of proposed method is verified through numerical examples

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

nonfragile control with guaranteed cost of t s fuzzy singular systems based on parallel distributed compensation this paper investigates the nonfragile guaranteed cost control problem for a class of uncertain nonlinear singular state delayed systems that is described by takagi sugeno models the upper bound of state delay is assumed to be available a linear quadratic cost function is specified as the performance index of the closed loop system attention is focused on the fuzzy state feedback controller design via parallel distributed compensation scheme which not only guarantees the regular impulse free and asymptotically stable of the closed loop fuzzy singular delay system but also provides an optimized upper bound of the guaranteed cost function for the possibility of feedback gain variation and all admissible uncertainties all derived sufficient conditions are given in terms of linear matrix inequalities some numerical examples are provided to illustrate the effectiveness of the proposed design scheme

critical behavior of sandpile models with sticky grains we revisit the question whether the critical behavior of sandpile models with sticky grains is in the directed percolation universality class our earlier theoretical arguments in favor supported by evidence from numerical simulations p k mohanty d dhar phys rev lett 89 2002 104303 have been disputed by bonachela et al phys rev e 74 2006 050102 for sandpiles with no preferred direction we discuss possible reasons for the discrepancy our new results of longer simulations of the one dimensional undirected model fully support our earlier conclusions

adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements this paper investigates the adaptive fuzzy backstepping control and h infty performance analysis for a class of nonlinear systems with sampled and delayed measurements in the control scheme a fuzzy estimator fe model is used to estimate the states of the controlled plant while the fuzzy logic systems are used to approximate the unknown nonlinear functions in the nonlinear system the controller is obtained based on the fe model by combining the backstepping technique with the classic adaptive fuzzy control method in the stability analysis all the signals in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded suub and the outputs of the system are proven to converge to a small neighborhood of origin furthermore the h infty performance is investigated and the outputs of the closed loop system are bounded in the h infty sense two examples are given to illustrate the effectiveness of the proposed control scheme

sampled data fuzzy stabilization of nonlinear systems under nonuniform sampling this paper investigates the sampled data fuzzy stabilization problem for a class of nonlinear systems that is exactly modeled in takagi sugeno fuzzy form at least locally a new method for designing parallel distribution compensation fuzzy controller is proposed which just requires that the nonlinear function is locally lipschitz by considering the sample and hold behavior of the system and using jensen s integral inequality an inequality constrain condition is derived from the locally lipschitz property further by defining a time dependent lyapunov krasovskii functional term a new technique instead of the use of s procedure is developed and stabilization conditions for state feedback and observer based output feedback under nonuniform sampling are obtained compared with the existing ones the new design method not only avoids the difficulty of finding exact upper bounds of asynchronous errors of mismatch membership functions but contains less conservatism and less numerical complexity as well finally some illustrative examples are given to show the effectiveness of the proposed design method and the significant improvement over the existing results

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

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

fuzzy approximation based adaptive control of nonlinear delayed systems with unknown dead zone this paper focuses on the problem of adaptive fuzzy control for a class of nonlinear systems without a strict feedback form a new adaptive fuzzy control scheme is proposed for nonlinear delayed systems with unknown dead zone nonlinearity control design is achieved by introducing a variable separation approach and employing the unique structural property of fuzzy logic systems the proposed adaptive fuzzy controller guarantees that all the closed loop signals are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin two simulation examples illustrate the effectiveness of the proposed approach

stability analysis and dynamic output feedback controller design of t s fuzzy systems with time varying delays and external disturbances abstract this paper investigates the stability analysis and takagi sugeno t s fuzzy dynamic output feedback control for a class of t s fuzzy systems with multiple time varying delays and unmatched disturbances firstly the t s fuzzy model is employed to represent the system based on the system input matrix and output matrix secondly the t s fuzzy dynamic output feedback controller is designed based on the t s fuzzy model thirdly the line integral fuzzy lyapunov functional is employed and the boundary information of membership functions is considered in the stability analysis compared with previous works the multiple time varying delays and unmatched disturbances are considered in the t s fuzzy system the t s fuzzy dynamic output feedback controller and t s fuzzy system employ the same number of fuzzy rules but different membership functions to relax the control design conditions the line integral fuzzy lyapunov functional is employed and the boundary information of membership functions is considered to obtain the less conservative stability conditions finally two simulation examples are performed and some comparison figures results are presented to show the effectiveness and advantage of proposed method respectively

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

on energy to peak filtering for nonuniformly sampled nonlinear systems a markovian jump system approach this paper focuses on the filter design for nonuniformly sampled nonlinear systems which can be approximated by takagi sugeno t s fuzzy systems the sampling periods of the measurements are time varying and the nonuniform observations of the outputs are modeled by a homogenous markov chain a mode dependent estimator with a fast sampling frequency is proposed such that the estimation can track the signal to be estimated with the nonuniformly sampled outputs the nonlinear systems are discretized with the fast sampling period by using an augmentation technique the corresponding stochastic estimation error system is obtained by studying the stochastic stability and the energy to peak performance of the estimation error system we derive the linear matrix inequality based sufficient conditions the parameters of the mode dependent estimator can be calculated by using the proposed iterative algorithm two examples are used to demonstrate the design procedure and the efficacy of the proposed design method

to transmit or not to transmit a discrete event triggered communication scheme for networked takagi sugeno fuzzy systems this paper first proposes a discrete event triggered communication scheme for a class of networked takagi sugeno t s fuzzy systems this scheme has two main features 1 whether or not the sampled state should be transmitted is determined by the current sampled state and the error between the current sampled state and the latest transmitted state compared with those in a periodic time triggered communication scheme the communication bandwidth utilization is considerably reduced while preserving the desired control performance and 2 it is a discrete event triggered communication scheme due to the fact that the triggered conditions are only measured and checked at a constant sampling period compared with a continuous event triggered communication scheme the special hardware for continuous measurement and computation is no longer needed second a networked t s fuzzy model is delicately constructed which not only considers nonuniform time scales in the networked t s fuzzy model and the parallel distributed compensation fuzzy control rules but includes the aforementioned state error as well third a stability criterion and a stabilization criterion about the networked t s fuzzy system are derived respectively the stability criterion and stabilization criterion can provide a tradeoff to balance the required communication resource and the desired performance lowering the desired performance allows the network to allocate more limited bandwidth to other nodes in need finally a numerical example is given to show the effectiveness of the proposed method

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

stabilization and separation principle of networked control systems using the t s fuzzy model approach this paper is concerned with the stabilization problem for a class of discrete time networked control systems ncss with bounded time delays and packet losses the controlled plant is represented by a takagi sugeno fuzzy model and both the state feedback control and output feedback control cases are considered by guaranteeing the decrement of lyapunov functional at each control signal updating step a less conservative stability condition for the state feedback ncss is derived and the corresponding stabilizing controller design method is also presented under an observer based framework the output feedback stabilization problem is further studied where the main contribution is the development of the separation principle for ncss illustrative examples are provided to show the advantage and effectiveness of the developed results

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

powers of the fundamental ideal in the witt ring abstract let k be a field of characteristic different from 2 in the algebraic theory of quadratic forms one studies the witt ring w k of equivalence classes of non degenerate quadratic forms the witt ring has a filtration given by the powers in k of the fundamental ideal i k of even dimensional forms the ideal in k is generated by the set pn k of n fold pfister forms a1 an ni 1 1 ai where ai k k 0 many questions about this filtration and its quotients have arisen in the study of w k the spectacular work of voevodsky together with his collaborative work with orlov and vishik allows one to answer many old questions the purpose of this paper is to indicate some of these solutions

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

a membership function dependent approach for stability analysis and controller synthesis of takagi sugeno models this paper presents a new approach for stability analysis and controller design of takagi sugeno ts models the analysis considers information derived from existing or induced order relations among the membership functions partitioning of the state space and the use of piecewise lyapunov functions pwlf arise naturally as a consequence of induced order relations conditions under the novel approach can be expressed as linear matrix inequalities lmis facilitating the inclusion of performance design examples are provided to show the advantages over the classical quadratic approach

relaxation technique for a t s fuzzy control design based on a continuous time fuzzy weighting dependent lyapunov function based on the fuzzy weighting dependent lyapunov function this paper proposes a method to drive the relaxed stabilization condition for continuous time takagi sugeno t s fuzzy control systems without resorting to elimination and bounding techniques here to achieve an improved robust h performance while enhancing the interactions among the fuzzy subsystems this paper proposes a valuable relaxation technique that is capable of incorporating the derivatives of fuzzy weighting functions to the relaxation process finally three examples are given to verify the effectiveness of the proposed method

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

exponential stabilization for a class of nonlinear parabolic pde systems via fuzzy control approach this paper deals with the exponential stabilization problem for a class of nonlinear spatially distributed processes that are modeled by semilinear parabolic partial differential equations pdes for which a finite number of actuators are used a fuzzy control design methodology is developed for these systems by combining the pde theory and the takagi sugeno t s fuzzy model based control technique initially a t s fuzzy parabolic pde model is proposed to accurately represent a semilinear parabolic pde system then based on the t s fuzzy model a lyapunov technique is used to design a continuous fuzzy state feedback controller such that the closed loop pde system is exponentially stable with a given decay rate the stabilization condition is presented in terms of a set of spatial differential linear matrix inequalities sdlmis furthermore a recursive algorithm is presented to solve the sdlmis via the existing linear matrix inequality optimization techniques finally numerical simulations on the temperature profile control of a catalytic rod are given to verify the effectiveness of the proposed design method

evidence for universality within the classes of deterministic and stochastic sandpile models recent numerical studies have provided evidence that within the family of conservative undirected sandpile models with short range dynamic rules deterministic models such as the bak tang wiesenfeld model p bak c tang and k wiesenfeld phys rev lett 59 381 1987 and stochastic models such as the manna model s s manna j phys a 24 l363 1991 belong to different universality classes in this paper we examine the universality within each of the two classes in two dimensions by numerical simulations to this end we consider additional deterministic and stochastic models and use an extended set of critical exponents scaling functions and geometrical features universal behavior is found within the class of deterministic abelian models as well as within the class of stochastic models which includes both abelian and non abelian models in addition it is observed that deterministic but non abelian models exhibit critical exponents that depend on a parameter namely they are nonuniversal

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

a novel approach to output feedback control of fuzzy stochastic systems this paper investigates the problem of hankel norm output feedback controller design for a class of t s fuzzy stochastic systems the full order output feedback controller design technique with the hankel norm performance is proposed by the fuzzy basis dependent lyapunov function approach and the conversion on the hankel norm controller parameters sufficient conditions are established to design the controllers such that the resulting closed loop system is stochastically stable and satisfies a prescribed performance the desired output feedback controller can be obtained by solving a convex optimization problem which can be efficiently solved by standard numerical algorithms finally a henon map system is used to illustrate the effectiveness of the proposed techniques

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

sticky grains do not change the universality class of isotropic sandpiles we revisit the sandpile model with sticky grains introduced by mohanty and dhar phys rev lett 89 104303 2002 whose scaling properties were claimed to be generically in the universality class of directed percolation for both isotropic and directed models while for directed models this conclusion is unquestionable for isotropic models we present strong evidence that the asymptotic scaling in the self organized regime in which a stationary critical state exists in the limit of slow driving and vanishing dissipation rate is like other stochastic sandpiles generically in the manna universality class this conclusion is drawn from extensive monte carlo simulations and is strengthened by the analysis of the langevin equations proposed by the same authors to account for this problem argued to converge upon coarse graining to the well established set of langevin equations for the manna class

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

filter design for interval type 2 fuzzy systems with d stability constraints under a unified frame this paper investigates the problem of filter design for interval type 2 it2 fuzzy systems with d stability constraints based on a new performance index attention is focused on solving the h infty l 2 l infty passive and dissipativity fuzzy filter design problems for it2 fuzzy systems with d stability constraints in a unified frame under the new performance index frame using lyapunov stability theory a novel type of it2 filter is designed such that the filtering error system guarantees the prescribed h infty l 2 l infty passive and dissipativity performance levels with d stability constraints the existence condition of the it2 filter is expressed as the convex optimization problem and the filter parameters in the condition can be solved by the standard software the it2 fuzzy model and it2 fuzzy filter do not need to share the same lower and upper membership functions finally a numerical example is provided to show the effectiveness of the proposed results

stability and stabilization of takagi sugeno fuzzy systems via sampled data and state quantized controller in this paper we investigate the problem of stability and stabilization for sampled data fuzzy systems with state quantization by using an input delay approach the sampled data fuzzy systems with state quantization are transformed into a continuous time system with a delay in the state the transformed system contains nondifferentiable time varying state delay based on some integral techniques some new stability and stabilization criteria are first proposed by a modified lyapunov functional furthermore in the case of no quantization some new stability and stabilization criteria are also obtained it is shown that the new stability and stabilization criteria can provide a larger upper bound of the sampling interval than some existing ones in the literature two simulation examples are given to show the effectiveness of the proposed design method

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

robust nonfragile h_ infty filtering of fuzzy systems with linear fractional parametric uncertainties this paper is concerned with the h filtering problem for continuous time takagi sugeno t s fuzzy systems different from existing results for fuzzy h filtering the proposed ones are toward uncertain fuzzy systems with linear fractional parametric uncertainties attention is focused on the design of a fuzzy filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by a descriptor representation approach two sufficient conditions for the h filter design are proposed in terms of linear matrix inequalities lmis when these lmis are feasible an explicit expression of the desired filter is given a simulation example will be given to show the efficiency of the proposed methods

pre specified performance based model reduction for time varying delay systems in fuzzy framework this paper attempts to provide a new solution to the model approximation problem for dynamic systems with time varying delays under the fuzzy framework for a given high order system our focus is on the construction of a reduced order model which approximates the original one in a prescribed error performance level and guarantees the asymptotic stability of the corresponding error system based on the reciprocally convex technique a less conservative stability condition is established for the dynamic error system with a given error performance index furthermore the reduced order model is eventually obtained by applying the projection approach which converts the model approximation into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm finally two numerical examples are provided to illustrate the effectiveness of the proposed method

annihilators of quadratic and bilinear forms over fields of characteristic two abstract let f be a field with 2 0 w f the witt ring of symmetric bilinear forms over f and w q f the w f module of quadratic forms over f let i f w f be the maximal ideal we compute explicitly in i f m and i m w q f the annihilators of n fold bilinear and quadratic pfister forms thereby answering positively in the case 2 0 certain conjectures stated by kruskemper in m kruskemper on annihilators in graded witt rings and in milnor s k theory in b jacob et al eds recent advances in real algebraic geometry and quadratic forms in contemp math vol 155 1994 pp 307 320

cohomological kernels of mixed extensions in characteristic 2 abstract let f be a field of characteristic 2 f m the space of m differential forms over f d f m 1 f m the differential operator and h 2 m 1 f the cokernel of the artin schreier operator f m f m d f m 1 given on generators by x d x 1 x 1 d x m x m x 2 x d x 1 x 1 d x m x m d f m 1 it was shown in 8 that given a multiquadratic purely inseparable extension l f and a separable quadratic extension k f then the kernel of the natural homomorphism h 2 m 1 f h 2 m 1 k l is equal to the sum of the kernels of the extensions l f and k f in this paper we extend this result to the compositum of a finite purely inseparable multiquadratic extension with a separable biquadratic extension and we prove that this splitting property of kernels is no longer true by computing the kernel of the compositum of a separable quadratic or biquadratic extension with a simple purely inseparable extension of arbitrary degree

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

from waves to avalanches two different mechanisms of sandpile dynamics time series resulting from wave decomposition show the existence of different correlation patterns for avalanche dynamics for the d 2 bak tang wisenfeld model long range correlations determine a modification of the wave size distribution under coarse graining in time and multifractal scaling for avalanches in the manna model the distribution of avalanche coincides with that of waves which are uncorrelated and obey finite size scaling a result expected also for the d 3 bak tang wiesenfeld sandpile

fault detection filtering for nonlinear switched stochastic systems in this note the fault detection filtering problem is solved for nonlinear switched stochastic system in the t s fuzzy framework our attention is concentrated on the construction of a robust fault detection technique to the nonlinear switched system with brownian motion based on observer based fault detection fuzzy filter as a residual generator the proposed fault detection is formulated as a fuzzy filtering problem by the utilization of the average dwell time technique and the piecewise lyapunov function technique the fuzzy parameter dependent fault detection filters are designed that guarantee the resulted error system to be mean square exponential stable with a weighted mathcal h infty error performance then the corresponding solvability condition for the fault detection fuzzy filter is also established by the linearization procedure technique finally simulation has been presented to show the effectiveness of the proposed fault detection technique

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