some upwinding techniques for finite element approximations of convection diffusion equations a uniform framework for the study of upwinding schemes is developed the standard finite element galerkin discretization is chosen as the reference discretization and differences between other discretization schemes and the reference are written as artificial diffusion terms these artificial diffusion terms are spanned by a four dimensional space of element diffusion matrices three basis matrices are symmetric rank one diffusion operators associated with the edges of the triangle the fourth basis matrix is skew symmetric and is associated with a rotation by 2 while finite volume discretizations may be written as upwinded galerkin methods the converse does not appear to be true our approach is used to examine several upwinding schemes including the streamline diffusion method the box method the scharfetter gummel discretization and a divergence free scheme

parameter dependent lmis in robust analysis characterization of homogeneous polynomially parameter dependent solutions via lmi relaxations this note investigates the robust stability of uncertain linear time invariant systems in polytopic domains by means of parameter dependent linear matrix inequality pd lmi conditions exploiting some algebraic properties provided by the uncertainty representation a systematic procedure to construct a family of finite dimensional lmi relaxations is provided the robust stability is assessed by means of the existence of a lyapunov function more specifically a homogeneous polynomially parameter dependent lyapunov hppdl function of arbitrary degree for a given degree if an hppdl solution exists a sequence of relaxations based on real algebraic properties provides sufficient lmi conditions of increasing precision and constant number of decision variables for the existence of an hppdl function which tend to the necessity alternatively if an hppdl solution of degree exists a sequence of relaxations which increases the number of variables and the number of lmis will provide an hppdl solution of larger degree the method proposed can be applied to determine homogeneous parameter dependent matrix solutions to a wide variety of pd lmis by transforming the infinite dimensional lmi problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite dimensional lmi conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter dependent solution of arbitrary degree illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature

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

local stability conditions for t s fuzzy time delay systems using a homogeneous polynomial approach abstract local stability conditions for time delay t s fuzzy systems are proposed by use of a homogeneous polynomial approach lesser conservatism can be expected based on the derived stability criteria due to the following three factors a a new fuzzy lyapunov krasovskii functional is constructed which contains a homogeneous polynomially parameter dependent matrix of degree 2 b the off diagonal matrix in reciprocal convexity lemma is extended to a homogeneous polynomially parameter dependent matrix and c local stability conditions for time delay t s fuzzy systems are proposed to overcome the difficulty of dealing with the time derivative of membership functions finally two numerical examples illustrate the effectiveness of the proposed methods

fuzzy job shop scheduling based on ranking level spl lambda 1 interval valued fuzzy numbers job shop scheduling is a difficult problem both theoretically and practically the theoretical problems stem from the search for optimal schedules subject to a limited number of constraints while the complexity of practical problems is due to the number and variety of constraints that are not rigid in the actual situations indeed in real world descriptions there are many vaguely formulated relations and imprecise data although the job shop scheduling problem has often been investigated very little of this research is concerned with the uncertainty characterized by the imprecision in problem variables in this paper we consider a fuzzy job shop scheduling problem with imprecise processing times we use fuzzy numbers and level spl lambda 1 interval valued fuzzy numbers for the representation of vague processing times this problem is similar to a fuzzy multiple criteria optimization problem the primary results obtained from this research are 1 signed distance ranking fuzzy numbers used to obtain a job shop scheduling problem in the fuzzy sense and 2 signed distance ranking level spl lambda 1 interval valued fuzzy numbers used to obtain another such problem

a globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions we analyze a new galerkin finite element method for numerically solving a linear convection dominated convection diffusion problem in two dimensions the method is shown to be convergent uniformly in the perturbation parameter of order h1 2 in a global energy norm which is stronger than the l2 norm this order is optimal in this norm for our choice of trial functions

new stability conditions based on piecewise fuzzy lyapunov functions and tensor product transformations improvements of recent stability conditions for continuous time takagi sugeno t s fuzzy systems are proposed the key idea is to bring together the so called local transformations of membership functions and new piecewise fuzzy lyapunov functions by relying on these special local transformations the associated linear matrix inequalities that are used to prove the system s stability can be relaxed without increasing the number of conditions in addition to enhance the usefulness of the proposed methodology one can choose between two different sets of conditions characterized by independence or dependence on known bounds of the membership functions time derivatives a standard example is presented to illustrate that the proposed method is able to provide substantial improvements in some cases

technical communique reducing conservativeness in recent stability conditions of ts fuzzy systems in this correspondence a new simple strategy for reducing the conservativeness in stability analysis of continuous time takagi sugeno fuzzy systems based on fuzzy lyapunov functions is proposed this new strategy generalizes previous results

brief paper quadratic boundedness via dynamic output feedback for constrained nonlinear systems in takagi sugeno s form this paper studies output feedback stabilization of takagi sugeno fuzzy systems with input or state constraint and bounded noise a dynamic output feedback controller is adopted rather than a controller based on the state observer the notion of quadratic boundedness specified by a common lyapunov matrix which is novel in fuzzy control is invoked to handle the noise under the proposed controller the state of the closed loop system is stabilizing to an ellipsoid specified by this common lyapunov matrix two numerical examples are given to show the effectiveness of the controller

a monotone finite element scheme for convection diffusion equations a simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection diffusion problems in any spatial dimension by properly averaging the pde coefficients on element edges the resulting finite element stiffness matrix is an m matrix under some mild assumption for the underlying generally unstructured finite element grids as a consequence the proposed edge averaged finite element scheme is particularly interesting for the discretization of convection dominated problems this scheme admits a simple variational formulation it is easy to analyze and it is also suitable for problems with a relatively smooth flux variable some simple numerical examples are given to demonstrate its effectiveness for convection dominated problems

control synthesis of discrete time t s fuzzy systems based on a novel non pdc control scheme this paper proposes relaxed stabilization conditions of discrete time nonlinear systems in the takagi sugeno t s fuzzy form by using the algebraic property of fuzzy membership functions a novel nonparallel distributed compensation non pdc control scheme is proposed based on a new class of fuzzy lyapunov functions thus relaxed stabilization conditions for the underlying closed loop fuzzy system are developed by applying a new slack variable technique in particular some existing fuzzy lyapunov functions and non pdc control schemes are special cases of the new lyapunov function and fuzzy control scheme respectively finally two numerical examples are provided to illustrate the effectiveness of the proposed method

robust sampled data fuzzy control for nonlinear systems and its applications free weight matrix method in this paper sampled data control is proposed to stabilize the nonlinear system which is expressed as a takagi sugeno t s fuzzy submodels based on suitable lyapunov krasovskii functional lkf along with new weighted integral inequalities the sufficient conditions are derived in terms of linear matrix inequalities which ensure the exponential stability of the proposed closed loop t s fuzzy system the peculiarity of this paper is as novel integral inequalities and lkf are proposed less conservative results are provided when compared to existing results besides that wind energy conversion systems chaotic systems and an inverted pendulum are validated with derived sufficient conditions the corresponding simulation results show the merit of the proposed results over the existing works

homogeneous polynomially nonquadratic stabilization of discrete time takagi sugeno systems via nonparallel distributed compensation law this paper considers stability of discrete time nonlinear systems in takagi sugeno t s form this problem has been studied for more than 20 years with many sufficient conditions and the asymptotically necessary and sufficient ans conditions with respect to the common quadratic lyapunov function having being obtained this paper considers general forms of homogeneous polynomially nonquadratic lyapunov hpnql function and homogeneous polynomially parameterized nonparallel distributed compensation hpp non pdc law by generalization of the procedure based on polya s theorem and techniques used for parameter dependent linear matrix inequality pd lmi which have been studied previously in different contexts ans stability conditions with respect to the general hpnql function are obtained

on estimation error bounds for receding horizon filters using quadratic boundedness quadratic boundedness is used to deal with stability and design of receding horizon estimators upper bounds on the norm of the estimation error have been found by means of invariant sets that can be constructed by using quadratic boundedness moreover these bounds are expressed in terms of linear matrix inequalities and are well suited to being minimized for the purpose of design

brief paper time varying discrete time linear systems with bounded rates of variation stability analysis and control design this paper investigates the problems of robust stability analysis and state feedback control design for discrete time linear systems with time varying parameters it is assumed that the time varying parameters lie inside a polytopic domain and have known bounds on their rate of variation a convex model is proposed to represent the parameters and their variations as a polytope and linear matrix inequality relaxations that take into account the bounds on the rates of parameter variations are proposed a feasible solution provides a parameter dependent lyapunov function with polynomial dependence on the parameters assuring the robust stability of this class of systems extensions to deal with robust control design as well as gain scheduling by state feedback are also provided in terms of linear matrix inequalities numerical examples illustrate the results

further improvement of periodic control approach for relaxed stabilization condition of discrete time takagi sugeno fuzzy systems in this paper we present a new stabilization condition for discrete time takagi sugeno t s fuzzy systems to this end the previously developed periodic nonparallel distributed compensation non pdc control law is extended to the more general one whose gain matrix has a block lower triangular matrix form a distinguished feature of the proposed control law is that it uses a discrete time feedback loop incorporating information from the previous states of the system the resultant stabilization condition is represented in the form of linear matrix inequalities lmis in addition we show that the proposed condition includes the existing one based on the periodic control approach as a particular case finally examples are given to show that the proposed condition provides less conservative results than those of the existing ones published in the literature

a fuzzy lyapunov function approach to estimating the domain of attraction for continuous time takagi sugeno fuzzy systems this paper deals with stability analysis and control design problems for continuous time takagi sugeno t s fuzzy systems the first aim is to present less conservative linear matrix inequality lmi conditions to design controllers and assess the stability the second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction da via lmis the results are based on the fuzzy lyapunov functions flfs and non parallel distributed compensation non pdc approaches finally examples illustrate the effectiveness and merits of the proposed methods

polynomial fuzzy observed state feedback stabilization via homogeneous lyapunov methods a homogeneously state dependent polynomial lyapunov function for an observed state feedback polynomial fuzzy control system is proposed from which an advanced sufficient sum of squares sos condition formulated in terms of state dependent matrix inequalities to achieve fuzzy stabilization is derived three main features compared with existing nonhomogeneously polynomial methods are as follows 1 homogeneous lyapunov function and its time derivative are nicely linked via the hessian matrix 2 removing the nonconvex obstacles on dot p x when deriving a nonhomogeneous lyapunov stabilization condition dot v x 3 separation principle holds since common p falls out as a special case the proposed homogeneous sos approach is placed ahead of the existing sos based methods found in polynomial fuzzy stabilization controls to verify the problem solving theories of the homogeneous polynomial method announced four examples are demonstrated to show the promising features of the approach adduced finally an appendix illustrating the solving procedure is added for clarification on how the examples are solved via sos

polynomial fuzzy models for nonlinear control a taylor series approach classical takagi sugeno t s fuzzy models are formed by convex combinations of linear consequent local models such fuzzy models can be obtained from nonlinear first principle equations by the well known sector nonlinearity modeling technique this paper extends the sector nonlinearity approach to the polynomial case this way generalized polynomial fuzzy models are obtained the new class of models is polynomial both in the membership functions and in the consequent models importantly t s models become a particular case of the proposed technique recent possibilities for stability analysis and controller synthesis are also discussed a set of examples shows that polynomial modeling is able to reduce conservativeness with respect to standard t s approaches as the degrees of the involved polynomials increase

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

a novel exponentially fitted triangular finite element method for an advection diffusion problem with boundary layers in this paper we develop an exponentially fitted finite element method for a singularly perturbed advection diffusion problem with a singular perturbation parameter this finite element method is based on a set of novel piecewise exponential basis functions constructed on unstructured triangular meshes the basis functions can not be expressed explicitly but the values of each of them and its associated flux at a point are determined by a set of two point boundary value problems which can be solved exactly a method for evaluating elements of the stiffness matrix is also proposed for the case that is small numerical results presented to validate the method show that the method is stable for a large range of it is also shown by the numerical results that the rate of convergence of the method in an energy norm is of orderh1 2when is small

dynamic output feedback predictive control of a takagi sugeno model with bounded disturbance this paper considers predictive control of a takagi sugeno fuzzy model with bounded disturbance strictly satisfying the input and state constraints the membership function dependent dynamic output feedback law as in a previous work is utilized the novelty lies in the following technical improvements for the notion of quadratic boundedness which specifies closed loop stability and invariance properties the full lyapunov matrix is utilized the real time ellipsoidal bound of true state is recursively optimized by invoking the s procedure some relaxation scalars being optimized by the norm bounding technique are introduced for better handling the input and state constraints the multistep approach where a sequence of dynamic output feedback laws are optimized at each sampling instant is given to improve the single step approach numerical examples are given to illustrate the effectiveness of the proposed controllers

brief paper approaches to extended non quadratic stability and stabilization conditions for discrete time takagi sugeno fuzzy systems this paper provides simple and effective linear matrix inequality lmi characterizations for the stability and stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this more general classes of non parallel distributed compensation non pdc control laws and non quadratic lyapunov functions are presented unlike the conventional non quadratic approaches using only current time normalized fuzzy weighting functions we consider not only the current time fuzzy weighting functions but also the l step past l 0 and one step ahead ones when constructing the control laws and lyapunov functions consequently by introducing additional decision variables it can be shown that the proposed conditions include the existing ones found in the literature as particular cases examples are given to demonstrate the effectiveness of the approaches

a triangulation approach to asymptotically exact conditions for fuzzy summations many takagi sugeno t s fuzzy control synthesis problems in the literature are expressed as the problem of finding decision variables in a double convex sum fuzzy summation of positive definite matrices matricespsila coefficients in the summation take values in the standard simplex this paper presents a triangulation approach to the problem of generating simplicial partitions of the standard simplex in order to set up a family of sufficient conditions and in parallel another family of necessary ones for fuzzy summations the conditions proposed in this paper are asymptotically exact as the size of the involved simplices decreases its conservativeness vanishes for a sufficiently fine partition sufficiently dense mesh of vertex points the set of conditions is in the form of linear matrix inequalities lmis for which efficient software is available

a finite element method for a singularly perturbed boundary value problem we examine the problem eu a x u b x u f x for 0 0 b x 2 4e 0 a b andf inc 2 0 1 e in 0 1 u 0 andu 1 given using finite elements and a discretized green s function we show that the el mistikawy and werle difference scheme on an equidistant mesh of widthh is uniformly second order accurate for this problem i e the nodal errors are bounded bych 2 wherec is independent ofh and e with a natural choice of trial functions uniform first order accuracy is obtained in thel 0 1 norm on choosing piecewise linear trial functions hat functions uniform first order accuracy is obtained in thel 1 0 1 norm

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

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

improvement on nonquadratic stabilization of discrete time takagi sugeno fuzzy systems multiple parameterization approach this paper presents the relaxed nonquadratic stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this we propose a new fuzzy controller and lyapunov function by generalizing the nonparallel distributed compensation non pdc control law and nonquadratic lyapunov function respectively by exploiting po lya s theorem and algebraic properties of a homogeneous polynomials of normalized fuzzy weighting functions an infinite family of sufficient conditions for the asymptotic stabilizability is derived these conditions are formulated in the format of linear matrix inequalities lmis and hence are numerically tractable via convex programming techniques finally an example is given to illustrate advantages of the proposed method

local stabilization of discrete time t s fuzzy systems with magnitude and energy bounded disturbances recently the local stability and local stabilization problems have been investigated by several authors for nonlinear systems described by takagi sugeno t s fuzzy systems in this paper we study the local stabilization problem for discrete time t s fuzzy systems with magnitude and energy bounded disturbances the control design problem is cast as a linear matrix inequality lmi optimization the state feedback controller is designed in such a way that if the initial state is within a certain domain then the state trajectories under bounded disturbances will not escape the fuzzy modelling region of the state space finally examples are given to demonstrate the validity of the proposed method

multi instant observer design of discrete time fuzzy systems a ranking based switching approach this paper generalizes recent results on multi instant observer design for discrete time takagi sugeno fuzzy systems through a valid ranking based switching approach the approach hereby develops a concentrated subdivision of spanning space composed of normalized fuzzy weighting functions and then substantially produces a new ranking based switching mechanism by taking advantage of this ranking based switching mechanism a class of new fuzzy multi instant observers are achieved and more relaxed design conditions with respect to the recent work can be obtained for ensuring the asymptotically stability of the developed state estimation error system two illustrative examples are provided to validate the effectiveness of the result given in this study

control law proposition for the stabilization of discrete takagi sugeno models this paper deals with the stabilization of a class of discrete nonlinear models namely those in the takagi sugeno form its main goal is to reduce conservatism of existing stabilization conditions using a special class of candidate lyapunov functions and an enhanced control law it is shown that the use of the aforementioned lyapunov function leads to less pessimistic solutions the usefulness of the new control law is shown through several examples

on the generalized local stability and local stabilization conditions for discrete time takagi sugeno fuzzy systems in this paper local stability and local stabilization problems are considered for discrete time nonlinear systems represented by takagi sugeno t s fuzzy systems improved methods to assess the local stability design locally stabilizing control laws and estimate the domain of attraction are developed in terms of single parameter minimization problems subject to linear matrix inequality lmi constraints the improvement is achieved by applying a convergent lmi relaxation technique to prove positivity of homogeneous polynomial parameter dependent matrices of arbitrary degree with variables in the simplex we also take advantage of the recently developed parameter variation modeling technique to deal with the case that the variation rate of the membership functions of the t s fuzzy systems is bounded and less than one finally several illustrative examples demonstrate the validity and efficiency of the proposed method

generalized nonquadratic stability of continuous time takagi sugeno models this paper provides generalized nonquadratic stability conditions for continuous time nonlinear models in the takagi sugeno ts form obtained by sector nonlinearity approach should global quadratic stability fail for a given nonlinear model the proposed approach allows the obtaining of progressively better estimations of the stability domain via local asymptotic conditions in the form of linear matrix inequalities lmis which are efficiently solved by convex optimization techniques illustrative examples are presented to emphasize the broadening capabilities of the new stability analysis

relaxed lmi based stability conditions for takagi sugeno fuzzy control systems using regional membership function shape dependent analysis approach this paper presents relaxed stability conditions for takagi sugeno t s fuzzy model based control systems it is assumed that the stability conditions are represented by some inequalities in the form of a p dimensional fuzzy summation to investigate the system stability the inequalities are expanded to n dimensional fuzzy summation n ges p the boundary and regional informations of membership functions are then utilized for relaxation of stability analysis results two analysis approaches are proposed in this paper the first approach is called the global membership function shape dependent approach in which the lower and upper bounds of the membership functions and its products from 2 to n in the full operating domain are considered in the stability analysis the second approach is named as the regional membership function shape dependent approach in which the operating region is partitioned to subregions and the boundary information of membership functions on each operating subregion is employed to facilitate the stability analysis in both approaches by the help of the boundary and or regional information of the membership functions some inequality constraints in the form of multidimensional fuzzy summation containing some slack matrices are constructed stability conditions in the form of linear matrix inequalities lmis are derived numerical examples are given to demonstrate the effectiveness of the proposed stability conditions

a new fuzzy lyapunov function approach for a takagi sugeno fuzzy control system design in this paper a new fuzzy lyapunov function approach is presented for a class of continuous time takagi sugeno fuzzy control system the proposed fuzzy lyapunov function is formulated as a line integral of a fuzzy vector which is a function of the state and it can be regarded as the work done from the origin to the current state in the fuzzy vector field unlike the approaches using a fuzzy blending of multiple quadratic lyapunov functions the time derivatives of membership functions do not appear in the proposed approach the effectiveness of the proposed approach is shown through numerical examples

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

local stabilization for discrete time t s fuzzy time delay systems with sensor fault abstract this paper focuses on a local stabilization problem for discrete time t s fuzzy time delay systems with sensor fault and external disturbances the main purpose is to synthesize a controller such that the state can be restricted into a pre specified region even when the system is subject to sensor fault and external disturbance first by restricting the reachable set into an ellipsoid set which is contained in the objective domain the system state is restricted into the objective area such that the local stabilization can be achieved second the differential mean value theorem is used to determine the bound of the deviation between the membership function of the system and that of the controller then the information of the deviation is employed for designing the controller different from some existing methods in the proposed method the influence of the sensor fault on the membership function of the controller has been fully considered and the information of aforementioned deviation is made full use of such that a less conservative stability criterion can be derived meanwhile due to the use of the differential mean value theorem the deviation bound can be calculated then the requirement where the deviation bound of is assumed to be previously known is removed finally an example is presented to verify the effectiveness of the proposed method

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

the finite element method with weighted basis functions for singularly perturbed convection diffusion problems in this paper we present a finite element method for singularly perturbed convection diffusion problems in both one and two dimensions based on a set of weighted basis functions constructed on unstructured meshes in 2d for the one dimensional case both first and second order schemes are discussed a technique for approximating fluxes is proposed some theoretical results on uniform convergence are obtained for the two dimensional case a first order scheme is constructed for problems with two singular perturbation parameters a technique is also developed in approximating fluxes in 2d this technique is used to simplify the calculation of the integrals in the stiffness matrix arising from the scheme which will save computational costs the numerical results support the theoretical results and demonstrate that the method is stable for a wide range of singular perturbation parameters

selective hbox scr h _2 and hbox scr h _ infty stabilization of takagi sugeno fuzzy systems this paper presents new results concerning the stability analysis and design of state feedback controllers for continuous time takagi sugeno t s fuzzy systems via fuzzy lyapunov functions the membership functions of the t s fuzzy systems are modeled in a space that is defined by the cartesian product of simplexes called a multisimplex if the time derivatives of the membership functions are bounded the bounds are used to construct a polytope that models the space of the time derivatives of the membership functions linear matrix inequality lmi relaxations that are based on polynomial matrices are provided for stability analysis and controller design extensions for the design of control laws that minimize upper bounds to h2 and h norms are also given the main novelty of this method is that it allows one to synthesize control gains which depends only on some premise variables that are selected by the designer numerical experiments illustrate the flexibility and advantages of the proposed method

robust observer design for unknown inputs takagi sugeno models this paper deals with the observer design for takagi sugeno t s fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system sufficient conditions to design an unknown input t s observer are given in linear matrix inequality lmi terms both continuous time and discrete time cases are studied relaxations are introduced by using intermediate variables extension to the case of unmeasured decision variables is also given a numerical example is given to illustrate the effectiveness of the given results

an exponentially fitted finite volume method for the numerical solution of 2d unsteady incompressible flow problems abstract in this paper we develop and test an exponentially fitted finite volume method for the numerical solution of the navier stokes equations describing 2d incompressible flows the method is based on an unstructured delaunay mesh and its dual dirichlet tessellation combined with a locally constant approximation to the flux this yields a piecewise exponential approximation to the exact solution numerical tests are presented for a linear advection diffusion problem with boundary layers the method is then applied to the driven cavity problem with reynolds numbers up to 10 4 the numerical results indicate that the method is robust for a wide range of values of the reynolds number in the case re 10 4 unsteady solutions are captured if the mesh is sufficiently fine

relaxed stability conditions for continuous time t s fuzzy control systems via augmented multi indexed matrix approach this paper is concerned with the problem of developing an advanced strategy to reduce the conservatism in stability analysis and control synthesis of continuous time takagi sugeno t s fuzzy systems a novel augmented multi indexed matrix approach is proposed to implement new right hand side slack variables technique for the homogenous polynomial setting combining with the finsler lemma with homogenous matrix lagrange multipliers convergent linear matrix inequality lmi relaxations for stability analysis are proposed by using the generalization of the polya theorem for the case of positive polynomials with matrix valued coefficients a new type of state feedback controller namely the homogeneous polynomially nonquadratic control law hpnqcl is developed to conceive less conservative stabilization conditions the obtained stability and stabilization conditions are further relaxed by using the proposed right hand side slack variables technique moreover the advantages over the existing control schemes are certificated in theory three numerical examples are also provided to illustrate the effectiveness of the proposed methods

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

stability analysis of polynomial fuzzy models via polynomial fuzzy lyapunov functions in this paper the stability of continuous time polynomial fuzzy models by means of a polynomial generalization of fuzzy lyapunov functions is studied fuzzy lyapunov functions have been fruitfully used in the literature for local analysis of takagi sugeno models a particular class of the polynomial fuzzy ones based on a recent taylor series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space it is shown that a refinement of the polynomial lyapunov function so as to make it share the fuzzy structure of the model proves advantageous conditions thus obtained are tested via available sos software

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a kind of controller synthesis method for fuzzy dynamic systems based on a piecewise smooth lyapunov function the basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the control laws can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software an example is given to illustrate the application of the proposed methods

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

a sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems this paper presents a sum of squares sos approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems the proposed sos based framework provides a number of innovations and improvements over the existing linear matrix inequality lmi based approaches to takagi sugeno t s fuzzy modeling and control first we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well known t s fuzzy modeling and control secondly we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial lyapunov functions that contain quadratic lyapunov functions as a special case hence the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing lmi based approaches to t s fuzzy modeling and control moreover the derived stability and stabilizability conditions are represented in terms of sos and can be numerically partially symbolically solved via the recently developed sostools to illustrate the validity and applicability of the proposed approach a number of analysis and design examples are provided the first example shows that the sos approach renders more relaxed stability results than those of both the lmi based approaches and a polynomial system approach the second example presents an extensive application of the sos approach in comparison with a piecewise lyapunov function approach the last example is a design exercise that demonstrates the viability of the sos based approach to synthesizing a stabilizing controller