improved linear matrix inequality approach to stability analysis of linear systems with interval time varying delays this paper investigates the problem of stability analysis for a class of linear systems with interval time varying delay in order to develop a less conservative stability condition a lyapunov krasovskii functional comprising novel integral terms is introduced convex combination idea is utilized to derive a stability criterion in terms of linear matrix inequalities lmis without any additional free weighting matrices which increase drastically the computational burden of the stability test numerical examples are presented to illustrate the superiority of the proposed approach compared to some existing ones in the literature

robust h stabilization for t s fuzzy systems with time varying delays and memory sampled data control abstract in this paper we address the robust h stabilization for t s fuzzy systems with time varying delays based on memory sampled data control by developing some new terms an improved piecewise lyapunov krasovskii functional lkf is constructed to take full advantage of characteristic about real sampling pattern furthermore some relaxed matrices proposed in the lkf are not necessarily positive definite by using the lkf and free matrix based fmb integral inequality some sufficient criteria are established to ensure the stability of fuzzy systems and reduce the influence of external disturbance with an h norm bound then the memory sampled data controller can be derived by solving a group of linear matrix inequalities lmis with the maximal sampling period finally a numerical example is given to demonstrate the benefits and the superiority of the approach proposed

stability and stabilization of t s fuzzy systems with time varying delays via augmented lyapunov krasovskii functionals this paper is concerned with the problem of stability and stabilization for takagi sugeno t s fuzzy systems with time varying delays by constructing a suitable lyapunov krasovskii functional sufficient conditions for ensuring the asymptotic stability and stabilization of the concerned fuzzy systems have been derived within the framework of linear matrix inequalities lmis the advantage and effectiveness of the proposed criteria will be shown through the comparison of maximum delay bounds with some results obtained by recently published papers via four numerical examples

robust h control of t s fuzzy systems with input time varying delays a delay partitioning method abstract addressed in this paper is the robust h control issue of t s fuzzy systems with input time varying delays by means of the delay partitioning method the delay interval is partitioned into multiple unequal subintervals whose lengths satisfy a geometric sequence on this basis a modified lyapunov krasovskii functional is presented to analyze asymptotic stability of the open loop system then a state feedback controller that ensures a prescribed h performance level for the closed loop system is proposed in linear matrix inequality format finally two numerical examples are given to illustrate the effectiveness and advantages of the obtained results

approaches to t s fuzzy affine model based reliable output feedback control for nonlinear ito stochastic systems this paper deals with the problem of reliable and robust mathscr h infty static output feedback sof controller synthesis for continuous time nonlinear stochastic systems with actuator faults the nonlinear stochastic plant is expressed by an ito type takagi sugeno fuzzy affine model with parametric uncertainties and a markov process is employed to model the occurrence of actuator fault the purpose is to design an admissible piecewise sof controller such that the resulting closed loop system is stochastically stable with a prescribed disturbance attenuation level in an mathscr h infty sense specifically based on a markovian lyapunov function combined with ito differential formula s procedure and some matrix inequality convexification procedures two new approaches to the reliable sof controller analysis and synthesis are proposed for the underlying stochastic fuzzy affine systems it is shown that the existence of desired reliable controllers is fully characterized in terms of strict linear matrix inequalities finally simulation examples are presented to illustrate the effectiveness and advantages of the developed methods

the ternary commutator obstruction for internal crossed modules abstract in finitely cocomplete homological categories co smash products give rise to possibly higher order commutators of subobjects we use binary and ternary co smash products and the associated commutators to give characterisations of internal crossed modules and internal categories respectively the ternary terms are redundant if the category has the smith is huq property which means that two equivalence relations on a given object commute precisely when their normalisations do in fact we show that the difference between the smith commutator of such relations and the huq commutator of their normalisations is measured by a ternary commutator so that the smith is huq property itself can be characterised by the relation between the latter two commutators this allows us to show that the category of loops does not have the smith is huq property which also implies that ternary commutators are generally not decomposable into nested binary ones thus in contexts where smith is huq need not hold we obtain a new description of internal categories beck modules and double central extensions as well as a decomposition formula for the smith commutator the ternary commutator now also appears in the hopf formula for the third homology with coefficients in the abelianisation functor

sampled data fuzzy control for a class of nonlinear parabolic distributed parameter systems under spatially point measurements abstract in this paper the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation pde systems via sampled data fuzzy control approach initially the nonlinear pde system is accurately represented by the takagi sugeno t s fuzzy pde model then based on the t s fuzzy pde model a novel time dependent lyapunov functional is used to design a sampled data fuzzy controller under spatially point measurements such that the closed loop fuzzy pde system is exponentially stable with a given decay rate the stabilization conditions are presented in terms of a set of linear matrix inequalities lmis finally simulation results on the control of the diffusion equation and the fitzhugh nagumo fhn equation to illustrate the effectiveness of the proposed design method

robust h control of uncertain fuzzy systems under time varying sampling robust h sampled data control for uncertain fuzzy systems is discussed in many practical situations a system is modeled as a continuous time fuzzy system while the control input is the zero order hold which can be represented as a piecewise continuous delay here we take a delay system approach to the h sampled data control problem the closed loop system with a sampled data state feedback controller becomes a system with time varying delay first h performance conditions for the closed loop system are given in terms of linear matrix inequalities lmis such conditions are derived by using the leibniz newton formula and free weighting matrix method for fuzzy time delay systems under the assumption that sampling time is not greater than some prescribed number then a design method for a robust h sampled data state feedback controller for uncertain fuzzy systems is proposed numerical examples are given to illustrate our robust h sampled data state feedback control design

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

unknown input observer design for one sided lipschitz discrete time systems subject to time delay in this paper we address the problem of unknown input observer design which simultaneously estimates state and unknown input of a class of nonlinear discrete time systems with time delay a novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one sided lipschitz and quadratically inner bounded conditions is proposed this approach also allows us to reconstruct the unknown inputs of the systems the nonlinear system is first transformed to a new system which can be decomposed into unknown input free and unknown input dependent subsystems the estimation problem is then reduced to designing observer for the unknown input free subsystem rather than full order observer design in this paper we propose observer design of reduced order which is more practical and cost effective by utilizing several mathematical techniques the time delay issue as well as the bilinear terms which often emerge when designing observers for nonlinear discrete time systems are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form two numerical examples are given to show the efficiency and high performance of our results

a bridging domain method for coupling continua with molecular dynamics abstract a bridging domain method for coupling continuum models with molecular models is described in this method the continuum and molecular domains are overlapped in a bridging subdomain where the hamiltonian is taken to be a linear combination of the continuum and molecular hamiltonians we enforce the compatibility in the bridging domain by lagrange multipliers or by the augmented lagrangian method an explicit algorithm for dynamic solutions is developed results show that this multiscale method can avoid spurious wave reflections at the molecular continuum interface without any additional filtering procedures even for problems with significant nonlinearities the method is also shown to naturally handle the coupling of the continuum energy equation with the molecular subdomain a multiple time step algorithm is also developed within this framework

new approach to delay dependent stability analysis and stabilization for continuous time fuzzy systems with time varying delay this paper is concerned with delay dependent stability analysis and stabilization problems for continuous time takagi and sugeno t s fuzzy systems with a time varying delay a new method for the delay dependent stability analysis and stabilization is suggested which is less conservative than other existing ones first based on a fuzzy lyapunov krasovskii functional lkf a delay dependent stability criterion is derived for the open loop fuzzy systems in the derivation process some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation and among the terms in the leibniz newton formula then a delay dependent stabilization condition based on the so called parallel distributed compensation pdc scheme is worked out for the closed loop fuzzy systems the proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities lmis and compared with the existing ones via two examples finally application to control of a truck trailer is also given to illustrate the effectiveness of the proposed design method

phonon absorbing boundary conditions for molecular dynamics with the goal of minimizing the domain size for molecular dynamics md simulations we develop a new class of absorbing boundary conditions abcs that mimic the phonon absorption properties of an unbounded exterior the proposed md abcs are extensions of perfectly matched discrete layers pmdls originally developed as an absorbing boundary condition for continuous wave propagation problems called md pmdl this extension carefully targets the absorption of phonons the high frequency waves whose propagation properties are completely different from continuous waves this paper presents the derivation of md pmdl for general lattice systems followed by explicit application to one dimensional and two dimensional square lattice systems the accuracy of md pmdl for phonon absorption is proven by analyzing reflection coefficients and demonstrated through numerical experiments unlike existing md abcs md pmdl is local in both space and time and thus more efficient based on their favorable properties it is concluded that md pmdl could provide a more effective alternative to existing md abcs

delay induced stability of vector second order systems via simple lyapunov functionals it is well known that some important classes of systems e g inverted pendulums oscillators double integrators that cannot be stabilized by a static output feedback may be stabilized by inserting an artificial time delay in the feedback static output feedback controllers have advantages over observer based controllers in the presence of uncertainties in the system matrices and or uncertain input output delays where the observer based design becomes complicated the existing lyapunov based methods that may treat the case of stabilizing delays and that lead to stability conditions in terms of linear matrix inequalities lmis suffer from high dimensionality of the resulting lmis with a large number of decision variables in this paper we suggest simple lyapunov functionals for vector second order systems with stabilizing delays that lead to reduced order lmis with a small number of decision variables moreover differently from the existing methods we show that the presented lmis are always feasible for small enough delays

stabilization by using artificial delays an lmi approach abstract static output feedback stabilization for the n th order vector differential equations by using artificial multiple delays is considered under assumption of the stabilizability of the system by a static feedback that depends on the output and its derivatives up to the order n 1 a delayed static output feedback is found that stabilizes the system the conditions for the stability analysis of the resulting closed loop system are given in terms of simple lmis it is shown that the lmis are always feasible for appropriately chosen gains and small enough delays robust stability analysis in the presence of uncertain time varying delays and stochastic perturbation of the system coefficients is provided numerical examples including chains of three and four integrators that are stabilized by static output feedbacks with multiple delays illustrate the efficiency of the method

h control for sampled data nonlinear systems described by takagi sugeno fuzzy systems in this paper we consider the design problem of output feedback h controllers for sampled data fuzzy systems we first transfer them into equivalent jump fuzzy systems we establish the so called bounded real lemma for jump fuzzy systems and give a design method of suboptimal output feedback h controllers in terms of two riccati inequalities with jumps we then apply the main results to the sampled data fuzzy systems and obtain a design method of suboptimal output feedback h controllers we give a numerical example and construct a suboptimal output feedback h controller

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

further results on stabilization of chaotic systems based on fuzzy memory sampled data control this note investigates sampled data control for chaotic systems a memory sampled data control scheme that involves a constant signal transmission delay is employed for the first time to tackle the stabilization problem for takagi sugeno fuzzy systems the advantage of the constructed lyapunov functional lies in the fact that it is neither necessarily positive on sampling intervals nor necessarily continuous at sampling instants by introducing a modified lyapunov functional that involves the state of a constant signal transmission delay a delay dependent stability criterion is derived so that the closed loop system is asymptotically stable the desired sampled data controller can be achieved by solving a set of linear matrix inequalities compared with the existing results a larger sampling period is obtained by this new approach a simulation example is presented to illustrate the effectiveness and conservatism reduction of the proposed scheme

a bridging domain and strain computation method for coupled atomistic continuum modelling of solids we present a multiscale method that couples atomistic models with continuum mechanics the method is based on an overlapping domain decomposition scheme constraints are imposed by a lagrange multiplier method to enforce displacement compatibility in the overlapping subdomain in which atomistic and continuum representations overlap an efficient version of the method is developed for cases where the continuum can be modelled as a linear elastic material an iterative scheme is utilized to optimize the coupled configuration conditions for the regularity of the constrained matrices are determined a method for computing strain in atomistic models and handshake domains is formulated based on a moving least square approximation which includes both extensional and angle bending terms it is shown that this method exactly computes the linear strain field applications to the fracture of defected single layer atomic sheets and nanotubes are given copyright 2006 john wiley sons ltd

new result on reliable h performance state estimation for memory static neural networks with stochastic sampled data communication abstract this work examines the h performance state estimation problem for memory static neural networks msnns with reliable state feedback stochastic sampled data control ssdc the purpose of presenting this study is to determine whether the h performance and criteria with less conservatism for stability could be gained by ssdc for msnns or not firstly we suppose that the sampling interval values follow bernoulli distribution and the probability of occurrence are teadfast constant then generalize it to a more universal form secondly on basis of considering the sampling input delay and its sawtooth structure characteristics a modified augmented lyapunov krasovskii functional lkf is constructed on account of the free matrix based integral inequality fmbii together with generalized free weighting matrix gfwm inequality which can reduce the conservatism of h performance criteria thirdly the expected estimator gain matrix can be designed in the light of the solution to linear matrix inequalities lmis finally an numerical example is given to check the superiority of the proposed msnns control design technique

event triggered sampling control for stability and stabilization of memristive neural networks with communication delays this paper investigates the global asymptotic stability and stabilization of memristive neural networks mnns with communication delays via event triggered sampling control first based on the novel approach in lemma 1 the concerned mnns are converted into traditional neural networks with uncertain parameters next a discrete event triggered sampling control scheme which only needs supervision of the system state at discrete instants is designed for mnns for the first time thanks to this controller the number of control updates could greatly reduce then by getting utmost out of the usable information on the actual sampling pattern a newly augmented lyapunov krasovskii functional lkf is constructed to formulate stability and stabilization criteria it should be mentioned that the lkf is positive definite only at endpoints of each subinterval of the holding intervals but not necessarily positive definite inside the holding intervals finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

initial tension in randomly disordered periodic lattices this paper is concerned with probabilistic analysis of initial member stress in geometrically imperfect regular lattice structures with periodic boundary conditions spatial invariance of the corresponding statistical parameters is shown to arise on the born von karman domains this allows analytical treatment of the problem where the parameters of stress distribution are obtained in a closed form several benchmark problems with beam and plate like lattices are considered and the results are verified by the direct monte carlo simulations behaviour of the standard deviation as a function of lattice repetitive cell number is investigated and dependence on the lattice structural redundancy is pointed out

an embedded statistical method for coupling molecular dynamics and finite element analyses the coupling of molecular dynamics md simulations with finite element methods fem yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales the theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks various specialized methods have been developed to solve particular classes of problems many of these methods link the kinematics of individual md atoms with finite element fe nodes at their common interface necessarily requiring that the fe mesh be refined to atomic resolution some of these coupling approaches also require simulations to be carried out at 0 k and restrict modelling to two dimensional material domains due to difficulties in simulating full three dimensional material processes in the present work a new approach to md fem coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain the method replaces a direct linkage of individual md atoms and fe nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each fe node in an interface region the fem and md computational systems are effectively independent and communicate only through an iterative update of their boundary conditions thus the method lends itself for use with any fem or md code with the use of statistical averages of the atomistic quantities to couple the two computational schemes the developed approach is referred to as an embedded statistical coupling method escm escm provides an enhanced coupling methodology that is inherently applicable to three dimensional domains avoids discretization of the continuum model to atomic scale resolution and permits finite temperature states to be applied published in 2009 by john wiley sons ltd

robust h sub spl infin control for fuzzy systems with frobenius norm bounded uncertainties in this paper we investigate the problem of robust h sub spl infin performance and stabilization for a class of uncertain fuzzy systems with frobenius norm bounded parameter uncertainties in all system matrices both continuous and discrete time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems unlike the bounded real lemma in the linear theory of robust h sub spl infin control where necessary and sufficient conditions were obtained only sufficient condition based on lyapunov method is shown furthermore connection between robust h sub spl infin problems involving uncertainty and standard uncertainty free h sub spl infin problems is established via matrix algebra as for controller synthesis a state feedback fuzzy control law is designed via relaxed linear matrix inequality lmi formulations

decentralized sampled data h fuzzy filter for nonlinear large scale systems this paper presents a decentralized sampled data h fuzzy filter design method for nonlinear large scale systems which are represented by a takagi sugeno t s fuzzy model based on the t s fuzzy model the error system between the nonlinear large scale system and the filter is obtained the discretization process of the error system is accomplished with the exact discrete time approach to eliminate the exact approximate mismatch by using the discrete time lyapunov sense the sufficient condition of the asymptotic stability for the error system is given and a prescribed level of the h norm is ensured to guarantee the h fuzzy filter performance finally numerical examples are given to show the effectiveness of the proposed methods

stability criteria for bam neural networks with leakage delays and probabilistic time varying delays this paper is concerned with the stability criteria for bidirectional associative memory bam neural networks with leakage time delay and probabilistic time varying delays by establishing a stochastic variable with bernoulli distribution the information of probabilistic time varying delay is transformed into the deterministic time varying delay with stochastic parameters based on the lyapunov krasovskii functional and stochastic analysis approach delay probability distribution dependent sufficient conditions are derived to achieve the globally asymptotically mean square stable of the considered bam neural networks the criteria are formulated in terms of a set of linear matrix inequalities lmis which can be checked efficiently by use of some standard numerical packages finally a numerical example and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results

baer sums in homological categories abstract we give a unified treatment of the baer sums in the context of efficiently homological categories which on the one hand contains any category of groups with multiple operators and more generally any semi abelian variety and on the other hand the category of hausdorff groups and more generally any category of semi abelian hausdorff algebras this gives rise to a generalized euclide s postulate and a five terms exact sequence

domain reduction method for atomistic simulations in this paper a quasi static formulation of the method of multi scale boundary conditions msbcs is derived and applied to atomistic simulations of carbon nano structures namely single graphene sheets and multi layered graphite this domain reduction method allows for the simulation of deformable boundaries in periodic atomic lattice structures reduces the effective size of the computational domain and consequently decreases the cost of computations the size of the reduced domain is determined by the value of the domain reduction parameter this parameter is related to the distance between the boundary of the reduced domain where msbcs are applied and the boundary of the full domain where the standard displacement boundary conditions are prescribed two types of multi scale boundary conditions are derived one for simulating in layer multi scale boundaries in a single graphene sheet and the other for simulating inter layer multi scale boundaries in multi layered graphite the method is tested on benchmark nano indentation problems and the results are consistent with the full domain solutions

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

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

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

absorbing boundary conditions for time harmonic wave propagation in discretized domains while many successful absorbing boundary conditions abcs are developed to simulate wave propagation into unbounded domains most of them ignore the effect of interior discretization and result in spurious reflections at the artificial boundary we tackle this problem by developing abcs directly for the discretized wave equation specifically we show that the discrete system mesh can be stretched in a non trivial way to preserve the discrete impedance at the interface similar to the perfectly matched layers pml for continuous wave equation the stretch is designed to introduce dissipation in the exterior resulting in a pml type abc for discrete media the paper includes detailed formulation of the new discrete abc along with the illustration of its effectiveness over continuous abcs with the help of error analysis and numerical experiments for time harmonic problems the improvement over continuous abcs is achieved without any computational overhead leading to the conclusion that the discrete abcs should be used in lieu of continuous abcs

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

design of h control for fuzzy time delay systems abstract in this paper the design problems of h output feedback controllers for takagi sugeno fuzzy time delay systems are considered we first introduce takagi sugeno fuzzy time delay systems and the h performance norm for stable fuzzy time delay systems we consider systems with multiple time delays in state we give a sufficient condition for the norm being less than a given number we then consider the h problems with output feedback controllers both memoryless controller and controller with memory are considered in the design of output feedback controllers the selection of the premise variables in the if then rules is important as for the premise variable we consider three cases where the premise variable is a given function the output and the state of the underlying system in the first two cases we give a design method of h controllers and sufficient conditions which guarantee the required h performance of the closed loop system in the last case we give an h controller for an approximation of the original system two examples are given to illustrate the theory

sampled data fuzzy control with space varying gains for nonlinear time delay parabolic pde systems abstract this paper introduces a sampled data fuzzy control sdfc with space varying gains for nonlinear time delay parabolic partial differential equation pde systems first a takagi sugeno t s fuzzy time delay parabolic pde model is employed to represent the nonlinear time delay pde system second with the aid of the t s fuzzy time delay pde model a sdfc design with space varying gains is developed in the formulation of space dependent linear matrix inequalities lmis by constructing an appropriate lyapunov functional which can stabilize exponentially the time delay pde system these stabilization conditions can be applied to either slowing varying time delay or fast varying one finally simulation results on two examples are presented to demonstrate the effectiveness of the proposed method

non reflecting boundary conditions for atomistic continuum and coupled atomistic continuum simulations summary we present a method to numerically calculate a non reflecting boundary condition which is applicable to atomistic continuum and coupled multiscale atomistic continuum simulations the method is based on the assumption that the forces near the domain boundary can be well represented as a linear function of the displacements and utilizes standard laplace and fourier transform techniques to eliminate the unnecessary degrees of freedom the eliminated degrees of freedom are accounted for in a time history kernel that can be calculated for arbitrary crystal lattices and interatomic potentials or regular finite element meshes using an automated numerical procedure the new theoretical developments presented in this work allow the application of the method to non nearest neighbour atomic interactions it is also demonstrated that the identical procedure can be used for finite element and mesh free simulations we illustrate the effectiveness of the method on a one dimensional model problem and calculate the time history kernel for fcc gold using the embedded atom method eam copyright 2005 john wiley sons ltd

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

on h control for linear systems with interval time varying delay this paper deals with the problem of delay dependent robust h control for linear time delay systems with norm bounded and possibly time varying uncertainty the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available and no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function based on an integral inequality which is introduced in this paper and lyapunov krasovskii functional approach a delay dependent bounded real lemma brl is first established without using model transformation and bounding techniques on the related cross product terms then employing the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop systems for all admissible uncertainties is proposed in terms of a linear matrix inequality lmi a numerical example is also given to illustrate the effectiveness of the proposed method

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

a novel approach to stability and stabilization of fuzzy sampled data markovian chaotic systems abstract this paper studies the problems of stability and stabilization of a class of markovian chaotic systems via fuzzy sampled data control different from some existing results the markovian jumping with general uncertain transition rates is considered for such systems a novel approach i e input delay dependent vector approach is proposed for the first time based on this approach an input delay dependent lyapunov krasovskii functional lkf with cubic function of input delay is successfully constructed and the convex combination technique is used with ease to derive stability and stabilization criteria compared with some existing stability and stabilization criteria for chaotic systems our results are not only less conservative but also with reduced calculation complexity finally the superiorities of proposed results are illustrated by two numerical examples

stability and stabilization for singular switching semi markovian jump systems with generally uncertain transition rates this paper studies the problems of stability and stabilization for a class of singular switching semi markovian jump systems the general transition rates in the semi markov process cover completely unknown and uncertain bounded as two special cases first sufficient conditions are developed to ensure the unforced system to be regular impulse free and exponentially mean square stable then by proposing a state feedback controller sufficient conditions in terms of strict linear matrix inequalities are derived to guarantee the closed loop system to be stochastically stabilziable finally a numerical example is provided to show the effectiveness of the obtained results

further refinements in stability conditions for time varying delay systems abstract this paper addresses the problem of assessing the stability of linear time invariant lti systems with time varying delay the first contribution is a new stability criterion specified as a negativity condition for a quadratic function parameterized by the delay this result mainly follows from an augmented affine parameter dependent lyapunov krasovskii functional which in turn takes advantages of convexity properties then as a second contribution we invoke a result from robust control literature to show how the proposed stability condition can be checked exactly in terms of linear matrix inequality lmi conditions the improvements obtained by the proposed refinements are illustrated via numerical examples drawn from the literature

fuzzy guaranteed cost control for nonlinear systems with time varying delay this paper focuses on the problem of guaranteed cost control for takagi sugeno t s fuzzy systems with time varying delayed state a linear quadratic cost function is considered as a performance index of the closed loop fuzzy system then the guaranteed cost control of the closed loop fuzzy system is discussed and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer based output feedback when these conditions which are given in terms of the feasibility of linear matrix inequalities lmis are satisfied the designed state feedback controller and observer based controller gain matrices can be obtained via a convex optimization problem two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

sampled data robust h control for t s fuzzy systems with time delay and uncertainties abstract this paper investigates sampled data robust h control for t s fuzzy systems with time delay and uncertainties by introducing the free weighting matrices to deal with the integral items and converting the coupling time varying matrix inequalities into a group of decoupling matrix inequalities an innovative delay dependent stabilization criterion is first presented then a sampled data h controller is designed to stabilize the t s fuzzy system to achieve the prescribed disturbance attenuation level which is dependent on both the size of state delay and upper bound of allowable sampling period since 1 the sawtooth structure of delay is fully considered 2 neither model transformation nor bounding techniques are employed in deriving the delay dependent results and 3 none of the integral items are arbitrarily ignored and magnified the less conservative results can be expected a practical application example is given to demonstrate the effectiveness of the proposed methods

stability analysis of sampled data systems via free matrix based time dependent discontinuous lyapunov approach in this paper a new time dependent discontinuous lyapunov functional namely free matrix based time dependent discontinuous fmbtdd lyapunov functional is introduced for stability analysis of sampled data systems first a modified free matrix based integral inequality mfmbii is derived based on the existing free matrix based integral inequality 1 and it is applied to develop a stability criterion for sampled data systems and then inspired by mfmbii fmbtdd term is established that leads to efficient stability conditions four numerical examples are given to demonstrate the effectiveness of the proposed methods

weighted commutators in semi abelian categories abstract we introduce new notions of weighted centrality and weighted commutators corresponding to each other in the same way as centrality of congruences and commutators do in the smith commutator theory both the huq commutator of subobjects and pedicchio s categorical generalization of smith commutator are special cases of our weighted commutators in fact we obtain them by taking the smallest and the largest weight respectively at the end of the paper we briefly consider the universal algebraic context in connection with an older work of the third author on the ideal theory version of the commutator theory

three dimensional bridging scale analysis of dynamic fracture this paper presents a three dimensional generalization of the bridging scale concurrent method a finite temperature multiple scale method that couples molecular dynamics md to finite elements fe the generalizations include the numerical calculation of the boundary condition acting upon the reduced md region as such boundary conditions are analytically intractable for realistic three dimensional crystal structures the formulation retains key advantages emphasized in previous papers particularly the compact size of the resulting time history kernel matrix the coupled fe and reduced md equations of motion are used to analyze dynamic fracture in a three dimensional fcc lattice where interesting physical phenomena such as crack branching are seen the multiple scale results are further compared to benchmark md simulations for verification purposes

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

improved delay dependent stability results of recurrent neural networks abstract by using the fact that the activation functions are sector bounded and a tighter inequality this paper presents a new method to the stability analysis of a class of recurrent neural networks rnns with time varying delays this method includes more the slope of activation functions and less variables matrices in constructed lyapunov krasovskii functional with the present stability conditions the computational burden and conservatism are largely reduced both theoretical analysis and numerical example are given to illustrate the effectiveness and the benefits of the proposed method

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

transmitting boundary conditions for 1d peridynamics summary the peridynamic theory reformulates the equations of continuum mechanics in terms of integro differential equations instead of partial differential equations it is not straightforward to apply the available artificial boundary conditions for continua to peridynamic modeling we therefore develop peridynamic transmitting boundary conditions ptbcs for one dimensional wave propagation differently from the previous method where the matching boundary condition is constructed for only one boundary material point the ptbcs are established by considering the interaction and exchange of information between a group of boundary material points and another group of inner material points the motion of the boundary material points is recursively constructed in terms of their locations and is determined through matching the peridynamic dispersion relation the effectiveness of the ptbcs is examined by reflection analyses numerical tests and numerical convergent conditions furthermore two way interfacial conditions are proposed the ptbcs are then applied to simulations of wave propagation in a bar with a defect a composite bar with interfaces and a domain with a seismic source all the analyses and applications demonstrate that the ptbcs can effectively remove undesired numerical reflections at artificial boundaries the methodology may be applied to modeling of wave propagation by other nonlocal theories this article is protected by copyright all rights reserved

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

an improved result on exponential stabilization of sampled data fuzzy systems this brief paper studies the exponential stabilization problem for the takagi sugeno fuzzy systems with a variable sampling different from previous results the gains of fuzzy state feedback controller adopted in this paper are time varying during two consecutive sampling instants which can contribute to the enlargement of the allowable sampling interval by choosing a suitable design parameter to reduce the design conservativeness a novel fuzzy time dependent lyapunov functional ftdlf is put forward to fully exploit the accessible information about the sampling pattern and the fuzzy basis functions moreover a more relaxed constraint condition is presented to ensure the positive definiteness of the ftdlf on sampling intervals by resorting to the novel ftdlf and the relaxed constraint condition new exponential stabilization criteria dependent on and independent of upper bounds on time derivatives of fuzzy basis functions are established by which a larger sampling interval can be achieved one example is offered to demonstrate the validity and superiorities of the obtained new results

delay dependent robust h sub spl infin control for t s fuzzy systems with time delay this paper focuses on the problem of delay dependent robust fuzzy control for a class of nonlinear delay systems via state feedback the takagi sugeno t s fuzzy model is adopted for representing a nonlinear system with time delayed state a delay dependent stabilization criterion is first presented then the methods of robust stabilization and robust h sub spl infin control are developed which are dependent on the size of the delay and are based on the solutions of linear matrix inequalities lmis finally a design example of robust h sub spl infin controller for uncertain nonlinear systems is given to illustrate the effectiveness of the approaches proposed in this paper

robust h_ infty control for uncertain takagi sugeno fuzzy systems with interval time varying delay this paper is concerned with the problem of robust hinfin control for a class of uncertain time delay fuzzy systems the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function the takagi sugeno t s uncertain fuzzy model with interval time varying delay is adopted based on the lyapunov krasovskii functional approach some delay dependent conditions for the existence of robust hinfin controller are formulated in the form of linear matrix inequalities lmis when these lmis are feasible an hinfin controller is presented a numerical example is given to demonstrate the effectiveness of the proposed method

an approach to h control of fuzzy dynamic systems this paper presents an approach to h control of a class of continuous time nonlinear systems which can be represented by a fuzzy dynamic model a suitable piecewise differentiable quadratic lyapunov function is used to establish asymptotic stability and h performance of the closed loop fuzzy control system a constructive algorithm is developed to obtain the h feedback control law which involves solving a set of suitable algebraic riccati equations an example is given to illustrate the application of the method

bridging multi scale method for localization problems abstract a bridging multi scale method is proposed for the analysis of a class of localization problems in which the micropolar continuum model is used to describe the localized deformation and the dynamic failure occurs only in a small number of localized regions it starts with a concurrent discretization of the entire domain with both coarse and fine scale finite element meshes the coarse scale mesh is employed to capture the nonlinear response with long wavelength outside the localized regions whereas the fine scale mesh captures the detailed physics of the localized deformation for both the coarse and fine scale meshes to coexist a bridging scale term is constructed so that the information common to both scales is correctly subtracted to achieve computational efficiency the localized regions are first identified by a preliminary calculation and the fine scale degrees of freedom dofs outside the localized regions are mathematically represented by the construction of dynamic interface conditions applied to the edges of these regions hence a large portion of the fine scale dofs are eliminated and the fine scale equations are reduced to a much smaller set with the added dynamic interface conditions the two way coupled coarse scale and reduced fine scale equations are then solved by a mixed time integration procedure applications to one dimensional and two dimensional dynamic shear localization problems are presented

a novel approach to reliable output feedback control of fuzzy affine systems with time delays and sensor faults this paper proposes a novel system augmentation approach to the delay dependent reliable piecewise affine mathscr h infty static output feedback control for nonlinear systems with time varying delay and sensor faults in the piecewise markovian lyapunov functional based framework the nonlinear plant is described by a continuous time takagi sugeno fuzzy affine model with parametric uncertainties and the sensor faults are characterized by a markov process specifically by applying a state input augmentation technique the original closed loop system is first reformulated into a descriptor fuzzy affine system based on a new piecewise markovian lyapunov krasovskii functional combined with a wirtinger based integral inequality improved reciprocally convex inequality and s procedure a novel bounded real lemma is then derived for the underlying closed loop system furthermore by taking advantage of the redundancy of descriptor system formulation together with a linearization procedure the piecewise affine controller synthesis is carried out it is shown that the desired piecewise affine controller gains can be attained by solving a linear matrix inequality based optimization problem finally simulation examples are performed to confirm the effectiveness and less conservatism of the presented approach

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

molecular dynamics boundary conditions for regular crystal lattices we present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice the method is based on a linearization in the vicinity of the boundary and utilizes a fourier and laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary this method is straightforward to implement numerically and thus can be automated for a general crystal lattice we show that this method reproduces the known kernel for a 1d linear chain and apply the approach to obtain the damping kernel matrices for two real crystal lattices the graphene and diamond structures of carbon

stabilization of chaotic systems under variable sampling and state quantized controller abstract this paper investigates the problem of stabilization for chaotic systems based on a t s fuzzy model under sampled data control and state quantization a novel lyapunov krasovskii functional lkf is introduced to the sampled data systems the benefit of the new approach is that the lkf develops more information about the actual sampling pattern in addition some symmetric matrices involved in the lkf are not required to be positive definite based on a recently introduced wirtinger based integral inequality that has been shown to be less conservative than jensen s inequality much less conservative stabilization conditions are obtained to ensure the maximal sampling period then the corresponding sampled data controllers can be synthesized by solving a set of linear matrix inequalities lmis finally an illustrative example is given to show the feasibility and effectiveness of the proposed method

slow state variables feedback stabilization for semi markov jump systems with singular perturbations the slow state variables feedback stabilization problem for semi markov jump discrete time systems with slow sampling singular perturbations is discussed in this work a new fairly comprehensive system model semi markov jump system with singular perturbations which is more general than markov jump model is employed to describe the phenomena of random abrupt changes in structure and parameters of the systems based on a slow state variables feedback control scheme a novel technique to design the desired controller is presented and the allowed maximum of singular perturbation parameter can be calculated with the help of the discrete time semi markov kernel approach some sojourn time dependent and less conservative sufficient conditions are established via a novel matrix decoupling technique to ensure the solvability of the problem to be addressed finally an illustrative example is given to show the superiority and usefulness of the proposed method

intrinsic centrality and associated classifying properties abstract the notion of central morphism is introduced in the very soft algebraic context of unital categories it reveals inside any such category an additive core which has a strong classifying potential

novel delay dependent robust h control of uncertain systems with distributed time varying delays this paper investigates the problem of delay dependent robust h control for a class of uncertain systems with distributed time varying delays the aim is to design a delay dependent robust h control which ensures robust asymptotic stability of the system the delay derivative dependent robust h control criteria are obtained in terms of linear matrix inequalities lmis numerical examples are given to illustrate the effectiveness of the proposed method the results are also compared with the existing results to show the conservativeness

h stabilization criterion with less complexity for nonuniform sampling fuzzy systems abstract this paper investigates the problem of h stabilization for nonuniform sampling fuzzy systems a method to design a fuzzy controller is proposed by taking the variation ranges of membership functions within sampling intervals into consideration to reduce the computational complexity jensen s integral inequality method is employed based on a well known inequality a convex combination technique is developed to deal with nonlinear time varying coefficients derived from jensen s integral inequality combining with capturing the characteristic of sampled data systems with a novel piecewise lyapunov krasovskii functional lkf a less complex and less conservative h stabilization criterion is formulated as linear matrix inequalities lmis which can be easily checked by using standard numerical software some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results

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

network based robust passive control for fuzzy systems with randomly occurring uncertainties this paper investigates the problem of robust passive control for networked fuzzy systems where randomly occurring uncertainties variable sampling intervals and constant network induced delay are taken into account a discontinuous lyapunov functional is introduced for the closed loop systems which takes full advantage of the sawtooth structure of the time varying interval delay induced by sample and hold and signal transmission a sufficient condition is proposed to ensure the closed loop system to be robustly stochastically passive then the problem of robust passive control is solved two examples are utilized to illustrate the advantages and effectiveness of the results that are proposed in this paper

sampled data synchronization of chaotic lur e systems via input delay dependent free matrix zero equality approach abstract this paper focuses on the sampled data synchronization problem of chaotic lur e systems clss by using sampled output of the systems with variable sampling rates one novel approach input delay dependent free matrix zero equality iddfmze approach is proposed for the first time the iddfmze approach can not only fully capture the available information on the actual sampling pattern but deploy more system information at the dynamic partitioning point a new lyapunov krasovskii functional lkf with some new terms is constructed which can use more information of the activation function at the dynamic partitioning point based on the presented iddfmze approach and the constructed lkf developed synchronization criterion is obtained in the form of linear matrix inequalities lmis the desired sampled data controller is designed under larger sampling period finally the superiority of proposed results is shown by two numerical examples