fuzzy theoretic approach to signals and systems static systems abstract fuzzy theoretic approach to signals and systems assumes all system variables and parameters as uncertain i e being characterized by membership functions develops a mathematical theory for analytically determining the membership functions on system variables and parameters derives algorithms for estimating the parameters of membership functions and establishes robustness and convergence properties of the estimation algorithms the membership functions are analytically determined via solving a variational optimization problem that maximizes the over uncertainties averaged log membership of the observed data around an initial guess this paper develops the analytical fuzzy theory for the particular case of a multi input single output static system affected by noises the theory facilitates designing an adaptive filtering algorithm the robustness of the adaptive filtering algorithm is proved theoretically via a mathematical analysis numerical experiments further demonstrate the robustness of the filtering algorithm a comparison of the algorithm with the state of art methods is made using the practical biomedical applications related to the modeling and analysis of heart rate signals for assessing the physiological state of an individual

event triggered fuzzy h control for a class of nonlinear networked control systems using the deviation bounds of asynchronous normalized membership functions this paper is concerned with the event triggered h control for a nonlinear networked control system a new event triggered transmission scheme is first proposed to reduce the network bandwidth utilization under this scheme the nonlinear networked control system is formulated as a takagi sugeno fuzzy threshold error dependent system with asynchronous normalized membership functions then by using the deviation bounds of asynchronous normalized membership functions some sufficient conditions on the existence of the parameters of the event triggered transmission scheme and the fuzzy controller are derived such that the takagi sugeno fuzzy threshold error dependent system with asynchronous normalized membership functions is asymptotically stable with a prescribed h attenuation level it is shown that the proposed design method can reduce the conservativeness of some existing results finally two examples are given to demonstrate the effectiveness of the proposed design method and the event triggered transmission scheme

h output feedback control design for uncertain fuzzy singularly perturbed systems an lmi approach this paper examines the problem of designing a robust h output feedback controller for a class of singularly perturbed systems described by a takagi sugeno fuzzy model based on a linear matrix inequality lmi approach lmi based sufficient conditions for the uncertain singularly perturbed nonlinear systems to have an h performance are derived to eliminate the ill conditioning caused by the interaction of slow and fast dynamic modes solutions to the problem are presented in terms of lmis which are independent of the singular perturbation the proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems a numerical example is provided to illustrate the design developed in this paper

approximation to a class of non autonomous systems by dynamic fuzzy inference marginal linearization method in this paper a dynamic fuzzy inference marginal linearization dfiml method is proposed for modeling nonlinear dynamic systems this method can transfer a group of input output data into a time variant fuzzy system with variable coefficients it is shown that solutions of time variant fuzzy systems generalized by dfiml method are universal approximators to solutions of a class of non autonomous systems also the analytical solutions of these time variant fuzzy systems can be obtained finally a simulation example is provided to illustrate the validity and potential of the developed techniques

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

a competitive strategy for distance aware online shape allocation we consider the following online allocation problem given a unit square s and a sequence of numbers n i 0 1 with j 0 i n j 1 at each step i select a region c i of previously unassigned area n i in s the objective is to make these regions compact in a distance aware sense minimize the maximum normalized average manhattan distance between points from the same set c i related location problems have received a considerable amount of attention in particular the problem of determining the optimal shape of a city i e allocating a single n i has been studied we present an online strategy based on an analysis of space filling curves for continuous shapes we prove a factor of 1 8092 and 1 7848 for discrete point sets

model approximation for discrete time state delay systems in the t s fuzzy framework this paper is concerned with the problem of h model approximation for discrete time takagi sugeno t s fuzzy time delay systems for a given stable t s fuzzy system our attention is focused on the construction of a reduced order model which not only approximates the original system well in an h performance but is also translated into a linear lower dimensional system by applying the delay partitioning approach a delay dependent sufficient condition is proposed for the asymptotic stability with an h error performance for the error system then the h model approximation problem is solved by using the projection approach which casts the model approximation into a sequential minimization problem subject to linear matrix inequality lmi constraints by employing the cone complementary linearization algorithm moreover by further extending the results h model approximation with special structures is obtained i e delay free model and zero order model finally two numerical examples are provided to illustrate the effectiveness of the proposed methods

fault detection and control co design for discrete time delayed fuzzy networked control systems subject to quantization and multiple packet dropouts abstract this paper investigates the problem of fault detection fd for discrete time delayed fuzzy networked control systems with quantization and packet dropouts different from existing results for fd the proposed ones are toward closed loop design problem that is the controller gain and the fault detection filter fdf gains are designed simultaneously the missing phenomenon is assumed to occur in the communication links for quantizer to fdf and controller to physical plant where the missing probability of packet dropouts is governed by an individual random binary distribution while the quantization errors are treated as sector bound uncertainties the discrete time fuzzy networked system is first transformed into the form of interconnection of two subsystems by applying an input output method and a two term approximation approach which is employed to approximate the time varying delay our attention is focused on the design of fuzzy fault detection filter ffdf such that for all data missing conditions and measurement quantization the residual system is stochastically stable with a guaranteed h performance sufficient conditions are first established via introducing some slack matrices to facilitate the fdf design procedure by eliminating the coupling between the lyapunov matrices and the system matrices numerical examples are provided to demonstrate the effectiveness and applicability of the proposed method

h_ infty fuzzy control with randomly occurring infinite distributed delays and channel fadings in this paper the h output feedback control problem is investigated for a class of discrete time fuzzy systems with randomly occurring infinite distributed delays and channel fadings a random variable obeying the bernoulli distribution is introduced to account for the probabilistic infinite distributed delays the stochastic rice fading model is employed to simultaneously describe the phenomena of random time delays and channel fadings via setting different values of the channel coefficients the aim of this paper is to design an h output feedback fuzzy controller such that the closed loop takagi sugeno t s fuzzy control system is exponentially mean square stable and the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of desired output feedback controllers ensuring both the exponential mean square stability and the prescribed h performance the cone complementarity linearization algorithm is utilized to cast the controller design problem into a sequential minimization one that is solvable by the semi definite programming method a simulation result is exploited to illustrate the usefulness and effectiveness of the proposed design technique

fault detection for fuzzy systems with intermittent measurements this paper investigates the problem of fault detection for takagi sugeno t s fuzzy systems with intermittent measurements the communication links between the plant and the fault detection filter are assumed to be imperfect i e data packet dropouts occur intermittently which appear typically in a network environment and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the unreliable communication links the aim is to design a fuzzy fault detection filter such that for all data missing conditions the residual system is stochastically stable and preserves a guaranteed performance the problem is solved through a basis dependent lyapunov function method which is less conservative than the quadratic approach the results are also extended to t s fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities which can be readily solved via standard numerical software two examples are provided to illustrate the usefulness and applicability of the developed theoretical results

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

discrete multiple delay advection reaction operators in this work we introduce a multiple delay term to the family of discrete operators known as advection reaction operators we present detailed quantitative information of the delay inclusion on the dynamics of the discrete dynamical systems with iteration functions given by the advection reaction operators those dynamical systems are infinite dimensional linear discrete dynamical systems and by using a matrix representation on the system we compute the iterates of such operators which are given by the powers of such matrices those matrices are sparse lower triangular matrices where only two subdiagonals are different than zero the entries of the power matrices are calculated explicitly and with the aid of some particular cases we can show their contained dynamical information

fuzzy model based sampled data control of chaotic systems a fuzzy time dependent lyapunov krasovskii functional approach this paper addresses the sampled data stabilization problem for chaotic systems represented by takagi sugeno t s fuzzy models if the upper bounds for the time derivative of membership functions are available combining the fuzzy blending for some quadratic functions together with the introduction of some new useful terms a novel fuzzy time dependent lyapunov krasovskii functional lkf is proposed to fully capture the available characteristics of the actual sampling pattern and membership functions simultaneously based on the proposed lkf a new criterion dependent on the upper bounds for the time derivative of membership functions is presented to guarantee the asymptotic stability of the whole closed loop system moreover a stability criterion independent of the upper bounds is also provided based on the corresponding common time dependent lkf then the designed fuzzy sampled data controller can be synthesized by analyzing the corresponding stabilization conditions moreover a search algorithm is provided to find the optimal tuning parameters finally one practical example of the lorenz system is given to illustrate that much less conservativeness can be achieved compared with the earlier results by using the corresponding common lkf and the results can be further improved when adopting the fuzzy time dependent lkf within large upper bounds

an approximate approach to h sup 2 optimal model reduction deals with the problem of computing an h sub 2 optimal reduced order model for a given stable multivariable linear system by way of orthogonal projection the problem is formulated as that of minimizing the h sub 2 model reduction cost over the stiefel manifold so that the stability constraint on reduced order models is automatically satisfied and thus totally avoided in the new problem formulation the closed form expression for the gradient of the cost over the manifold is derived from which a gradient flow results as an ordinary differential equation ode a number of nice properties about such a flow are established furthermore two explicit iterative convergent algorithms are developed from the flow one has a constant step size and the other has a varying step size and is much more efficient both of them inherit the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model reduction cost is decreasing to minima along the iterates a procedure for closing the gap between the original and modified problem is proposed in the symmetric case the two problems are shown to be equivalent numerical examples are presented to illustrate the effectiveness of the proposed algorithms as well as convergence

adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on a small gain approach in this paper an adaptive fuzzy robust output feedback control problem is considered for a class of single input and single output nonlinear systems in a strict feedback form the considered systems possess the unstructured uncertainties unknown dead zone and the dynamics uncertainties and they do not assume the states being available for the controller design in the controller design fuzzy logic systems are first used to approximate the unstructured uncertainties and by utilizing the information of the bounds of the dead zone slopes and treating the time varying inputs coefficients as a system uncertainty a fuzzy state observer is designed to estimate the unmeasured states by combining a backstepping technique with a nonlinear small gain approach a new adaptive fuzzy robust output feedback control has been developed it is proved that the proposed fuzzy adaptive control approach can guarantee the semiglobal uniform ultimate boundedness for all the solutions of the closed loop systems simulation studies and comparisons with previous methods are included to illustrate the effectiveness of the proposed approach

reachable set estimation of t s fuzzy systems with time varying delay in this paper the reachable set estimation problem is investigated for delayed discrete time takagi sugeno fuzzy systems with bounded input disturbances and nonzero initial conditions a reachable set estimation condition is derived by using the reciprocally convex combination approach to bound the forward difference of triple summable terms the derived condition guarantees that all the states of the system with the initial conditions from some domain are bounded in a compact set and all the states from other domain converge exponentially within another compact set moreover a less conservative stability condition is also obtained the effectiveness and the reduced conservatism of the proposed results are illustrated by numerical examples

static output feedback mathscr h _ bm infty control of continuous time t s fuzzy affine systems via piecewise lyapunov functions this paper investigates the problem of robust h output feedback control for a class of continuous time takagi sugeno t s fuzzy affine dynamic systems with parametric uncertainties and input constraints the objective is to design a suitable constrained piecewise affine static output feedback controller guaranteeing the asymptotic stability of the resulting closed loop fuzzy control system with a prescribed h disturbance attenuation level based on a smooth piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexification techniques some new results are developed for static output feedback controller synthesis of the underlying continuous time t s fuzzy affine systems it is shown that the controller gains can be obtained by solving a set of linear matrix inequalities lmis finally three examples are provided to illustrate the effectiveness of the proposed methods

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

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

model approximation for fuzzy switched systems with stochastic perturbation in this paper the model approximation problem is investigated for a takagi sugeno fuzzy switched system with stochastic disturbance for a high order considered system our attention is focused on the construction of a reduced order model which not only approximates the original system well with a hankel norm performance but translates it into a lower dimensional fuzzy switched system as well by using the average dwell time approach and the piecewise lyapunov function technique a sufficient condition is first proposed to guarantee the mean square exponential stability with a hankel norm error performance for the error system the model approximation is then converted into a convex optimization problem by using a linearization procedure finally simulations are provided to illustrate the effectiveness of the proposed theory

h model reduction of markovian jump linear systems abstract in this paper the h model reduction problem for linear systems that possess randomly jumping parameters is studied the development includes both the continuous and discrete cases it is shown that the reduced order models exist if a set of matrix inequalities is feasible an effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the model reduction solutions using the numerical solutions of the matrix inequalities the reduced order models can be obtained an example is given to illustrate the proposed model reduction 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

a novel observer based output feedback controller design for discrete time fuzzy systems this paper addresses the problem of observer based output feedback controller designs for discrete time t s fuzzy systems based on a relaxed approach in which the fuzzy lyapunov functions are used different from the existing two step method a single step linear matrix inequality method is provided for the observer based controller design it is shown that the controller and observer parameters can be obtained by solving a set of strict linear matrix inequalities that are numerically feasible with commercially available software the new design method not only overcomes the drawback induced by the two step approach but also provides less conservative results over some existing results finally the effectiveness of the proposed approach is demonstrated by an example

h model reduction for discrete time delay systems delay independent and dependent approaches this paper investigates the problem of h model reduction for linear discrete time state delay systems for a given stable system our attention is focused on the construction of reduced order models which guarantee the corresponding error system to be asymptotically stable and have a prescribed h error performance both delay independent and dependent approaches are developed with sufficient conditions obtained for the existence of admissible reduced order solutions since these obtained conditions are not expressed as strict linear matrix inequalities lmis the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to lmi constraints which can be readily solved in standard numerical software in addition the development of reduced order models with special structures such as delay free models and zeroth order models is also addressed the approximation methods presented in this paper can be further extended to cope with systems with unc

finite frequency model reduction of takagi sugeno fuzzy systems this paper considers the model reduction problem for continuous time takagi sugeno t s fuzzy systems different from existing full frequency methods a finite frequency model reduction method is proposed in this paper the proposed method can get a better approximation performance when input signals belong to a finite frequency domain to this end a finite frequency h infty performance index is first defined then a sufficient finite frequency performance analysis condition is derived by the aid of parseval s theorem and quadratic functions based on this condition and projection lemma three model reduction algorithms for t s fuzzy systems with input signals in low frequency middle frequency and high frequency domain are obtained respectively finally an example is given to illustrate the effectiveness of the proposed method

ℋ model reduction for linear parameter varying systems with distributed delay this paper is concerned with the model reduction for linear parameter varying lpv systems with both discrete and distributed delays for a given stable system our attention is focused on the construction of reduced order models which approximate the original system well in an norm sense first a sufficient condition is proposed for the asymptotic stability with an performance of the error system by using the parameter dependent lyapunov functional method then the decoupling technique is applied such that there does not exist any product term between the lyapunov matrices and the system matrices in the parametrised linear matrix inequality plmi constraints thus a new sufficient condition is obtained based on the new condition two different approaches are developed to solve the model reduction problem one is the convex linearisation approach and the other is the projection approach finally a numerical example is provided to demonstrate the effectiveness of the proposed design method

sliding mode control of quantized systems against bounded disturbances abstract this paper investigates the sliding mode control problem of quantized systems with simultaneous input and output disturbances in a network environment the output measurements are supposed to be quantized with a logarithmic strategy before transmitting over the digital channels the main difficulties in this design are as follows 1 there exists input output disturbances and state time delay in the plant under consideration such that model discretization is difficult to be implemented the design work is therefore forbidden to be considered in continuous time domain 2 the quantized signals piecewise constants cannot be used to synthesize a continuous time sliding mode surface 3 traditional observer technique is not effective to handle output disturbances in this paper a filtering based technique is proposed to solve these difficulties based on which a sliding mode observer based control scheme is developed to stabilize the resulting closed loop systems finally the effectiveness of the proposed methodology is illustrated via a numerical example

robust finite time h control for uncertain discrete jump systems with time delay abstract this paper addresses the robust finite time h control problem for a family of uncertain discrete time markovian jump systems with time delay initially the concepts of stochastic finite time boundedness and stochastic h finite time stabilization are given then a stochastic finite time h controller is designed such that the underlying closed loop discrete jump time delay system is stochastic finite time boundedness and satisfies a prescribed h performance level in some given finite time interval based on lyapunov approach sufficient criteria on the stochastic h finite time stabilization are established for the solvability of the problem which can be handled by a feasibility problem in the form of linear matrix inequalities with a fixed parameter finally simulation examples are presented to demonstrate the validity of the developed techniques

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

stability and stabilization of delayed t s fuzzy systems a delay partitioning approach this paper proposes a new approach namely the delay partitioning approach to solving the problems of stability analysis and stabilization for continuous time delay takagi sugeno fuzzy systems based on the idea of delay fractioning a new method is proposed for the delay dependent stability analysis of fuzzy time delay systems due to the instrumental idea of delay partitioning the proposed stability condition is much less conservative than most of the existing results the conservatism reduction becomes more obvious with the partitioning getting thinner based on this the problem of stabilization via the so called parallel distributed compensation scheme is also solved both the stability and stabilization results are further extended to time delay fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities lmis which can be readily solved via standard numerical software the advantage of the results proposed in this paper lies in their reduced conservatism as shown via detailed illustrative examples the idea of delay partitioning is well demonstrated to be efficient for conservatism reduction and could be extended to solving other problems related to fuzzy delay systems

dob fuzzy controller design for non gaussian stochastic distribution systems using two step fuzzy identification this paper presents a novel non gaussian stochastic control framework for the problem of disturbance estimation and rejection by combining fuzzy identification technology with disturbance observer design first fuzzy logic models are used to approximate the output probability density functions pdfs of non gaussian processes such that the task of pdf shape control can be reduced to a fuzzy weight dynamics modeling and control problem next takagi sugeno fuzzy models with multiple disturbances are employed to describe the nonlinear relations between fuzzy weight dynamics and the control input in which a novel disturbance observer based pi type fuzzy feedback controller is designed to ensure the system stability and convergence of the tracking error to zero meanwhile the disturbance estimation and attenuation performance as well as the state constrained requirement can also be guaranteed moreover the novel composite observer is constructed by augmenting the disturbance estimation into the full state estimation the satisfactory tracking performance and full state observation effect can be achieved by the designed optimization algorithm finally simulations for paper making process are given to show the efficiency of the proposed approach

on h2 model reduction of bilinear systems the h 2 model reduction problem for continuous time bilinear systems is studied in this paper by defining the h 2 norm of bilinear systems in terms of the state space matrices the h 2 model reduction error is computed via the reachability or observability gramian necessary conditions for the reduced order bilinear models to be h 2 optimal are given the gradient flow approach is used to obtain the solution of the h 2 model reduction problem the formulation allows certain properties of the original models to be preserved in the reduced order models the model reduction procedure developed can also be applied to finite dimensional linear time invariant systems a numerical example is employed to illustrate the effectiveness of the proposed method

an approach to observer design of continuous time takagi sugeno fuzzy model with bounded disturbances this paper addresses the problem of designing the observer for a class of nonlinear systems by using the t s takagi sugeno fuzzy model first two lemmas are obtained to demonstrate how to design the observer then based on the non quadratic lyapunov function a new method is proposed to locally stabilize the t s fuzzy system the new method can be applied to any t s models no matter whether the rules are even or odd naturally the new method is extended to get some lmis linear matrix inequalities to design the observer for practical reason the disturbances considered in this paper are bounded by magnitude and energy finally three examples are given to illustrate the effectiveness of the new approach

reliable h_ infty control for discrete time fuzzy systems with infinite distributed delay in this paper the problem of reliable h control is investigated for discrete time takagi sugeno t s fuzzy systems with infinite distributed delay and actuator faults a discrete time homogeneous markov chain is used to represent the stochastic behavior of actuator faults in terms of a stochastic fuzzy lyapunov functional a sufficient condition is proposed to ensure that the resultant closed loop system is exponentially stable in the mean square sense with an h performance index based on the derived condition the reliable h control problem is solved and an explicit expression of the desired controller is also given the case of no failure in the actuator is also considered a numerical example is given to demonstrate that our results are effective and less conservative

local analysis of continuous time takagi sugeno fuzzy system with disturbances bounded by magnitude or energy a lagrange multiplier method abstract this paper is concerned with the problem of computing the bounds of disturbances for continuous time takagi sugeno fuzzy model two kinds of disturbances are investigated by applying the non parallel distributed compensation non pdc law non quadratic lyapunov function and lagrange multiplier method one is bounded by magnitude the other is bounded by energy if the exogenous disturbances are bounded by magnitude the maximal value of the magnitude under which the closed loop system can be controlled is obtained by solving an optimization problem on the other hand if the disturbances are bounded by energy except for the maximal bound some conditions are derived to get two local regions a smaller and a bigger such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set where the original system can be represented as t s model exactly in the end the effectiveness of the proposed results is demonstrated by two examples

hankel norm model reduction of discrete time interval type 2 t s fuzzy systems with state delay this article focuses on the model reduction problem of discrete time time delay interval type 2 takagi sugeno t s fuzzy systems compared with the type 1 t s fuzzy system the interval type 2 t s fuzzy system has more advantages in expressing nonlinearity and capturing uncertainties in addition in order to simplify the analysis process complex high order systems can be approximated as low order systems which is called model reduction in previous studies there are few researches on model reduction of the interval type 2 t s fuzzy system with time delay hankel norm is adopted to limit the error after model reduction based on jensen s inequality a linear matrix inequality lmi condition for the hankel norm performance of the error system is obtained a membership function dependent method based on piecewise linear membership functions is utilized to deal with mismatched membership functions where information of membership functions will be used for relaxing analysis results next by a convex linearization design the model reduction problem is formulated as a convex lmi feasibility optimization condition numerical examples are given to verify the validity of the analysis

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory