亚洲免费av电影一区二区三区,日韩爱爱视频,51精品视频一区二区三区,91视频爱爱,日韩欧美在线播放视频,中文字幕少妇AV,亚洲电影中文字幕,久久久久亚洲av成人网址,久久综合视频网站,国产在线不卡免费播放

        ?

        Exponential stabilityfor switched systems with mutiple time-varingdelays

        2013-11-01 07:17:18zhong
        關鍵詞:師范大學沈陽學報

        , zhong

        (School of Mathmatics and System Science,Shenyang Normal University,Shenyang 110034,China)

        0 Introduction

        As an important class of hybrid dynamical systems,switched systems consist of a family of subsystems described by differential or difference eauations and a logical rule that orchestrates the switching mechanism between these subsystems.Switched systems arise in many practical models in manufacturing,communication networks,automotive engine control,chemical processes and so on[1-2].

        During the previous decade,the stability problem of switched linear systems has attracted a lot of attention[3-4].For stability issues,two main problems haves been investigated in known literatures.One is to find conditions that guarantee asymptotic stability of the switched systems for arbitrary switching.The other is to identify those switching signals for which the switched systems is asymptotically stable if it is not asymptotically stable for arbitrary switching.The main approach for stability analysis relies on the use of Lyapunov-Krasovskii functionals and LMIs approach for construting common Lyapunov function[5].

        Time delay is often encountered in various engineering systems.It has been well recognised that the presence of time delay may result instability and poor performance of a control system[6-9].For switched systems,because of the complicated behavior caused by the interaction between the continous dynamics and discrete switching,the problem of time delays is more difficult to study,while it has a wider range of application in engineering.So reseaching the switched systems with timedelay has more important theoretical and practical significance.

        Recently,some results have appeared on stability analysis,controller and robust filtering design for switched systems with time delay in the open literature[10-14].Sun et al.[10]studied the stability and L2-gain analysis for a class of switched systems with time-delay.In terms of a set of linear matrix inequalities,some sufficient conditions are obtained by average dwell time.The exponential stability problem was considered in[17]for switched linear system with impulsive effects by using matrix measure concept.Although many important results have been obtained for switched linear systems,there are few results concerning the stability of the system with multiple time-varing delays[17].The paper[15]just considered the switched systems with multiple time-delay,and the time-varing delay is not considered.

        In this paper,we investigate the problem of the exponential stability for switched systems with multiple time-varing delays.Based on a piecewise Lyapunov-Krasovskii functional,and taking the measure of average dwell time,a new sufficent condition for robust exponential stability is obtained.The sufficient conditions are given in the form of LMIs that can be solved easily.The result is proven to be valid by the simulation at last.

        1 preliminaries

        Consider the following switched systems which consist of m subsystems with multiple timevarying delays.Without the general,we just consider the systems with two time-varying delays as:

        Wherex(t)∈Rnis the state,σ(t):[0,+∞]→M={1,2,…,m}is switching signal;mis a natural number that denotes the number of the subsystems.Ai∈Rn×n,A1i∈Rn×n,A2i∈Rn×nare systems matrices and time-varying delay matrices with appropriate dimensions forith subsystem.The initial condition is continuous vector valued function int∈[-h(huán),0],h∈max{hi}.di(t)is the time-varying delays of the system and satisfies following conditions:

        If the swiched systems have structural uncertainties,they can be described as following:

        And the time-varying structural uncertainties have the form as following:

        WhereDi,Ei,E1iandE2iare contant matrice with appropriate dimensions.Fi(t)are time-varying unknown matrices,and satisfyingFTiFi≤I,?t∈R,i∈M,whichIis an identical matrix with apropriate dimensions.

        Lemma 1[14]Assume that H1holds,then,for anyx(t)solution to system (1)and constant matrixesWi>0,the following inequality holds:

        Lemma 2[15]For any matricesP,E,F(xiàn),HwithP>0,F(xiàn)TF≤I,and scalarε>0,one has:EFH+HTFTET≤ε-1EET+εHTH.

        Corresponding to the switching signalσ(t),we have the swiching sequence:

        2 Main results

        2.1 Exponential stability of switched systems

        The sufficient condition of the multiple time-varying delays exponential stability for the switched systems(1)is given below.

        Theorem 1For scalarsh1>0,h2>0,andα>0,if there exist matricesPi>0,Q1i>0,Q2i>0,Z1i>0Z2i>0such that the following LMIs hold:

        Then the switched system (1)are exponentially stable for any switching law satisfying the average dwell timeTα>=lnμ/α.

        Further more,the decay of the state is

        Therefore,theorem 1holds.

        2.2 Robust exponential stability of the uncertian switched systems

        The sufficient condition of robust exponential stability for the uncentain switched systems(2)given as following.

        Theorem 2For scalarsh1>0,h2>0,andα>0,if there exist matricesPi>0,Q1i>0,Q2i>0,Z1i>0,Z2i>0,such that the following LMIs hold,then the systems(2)is robust exponential stability.

        And the uncertain swiched systems(2)are saitisfying the average dwell timeTα>T*α=lnμ/α.

        Furthermore,the decay of the state is

        From the lemma 2,there exist a positive scaleεi(i∈M),we can obtain that the above inequality holds if and only if(9)is holded.

        The equality(9)holds if and only if(7)holds through Shur complementary lemma.The last proof is similar to the process of theorem 1.

        3 Numerical example and simulatiom

        Example:Comsider system (1)for the following parameters:

        Chooseα=0.5,μ=1.2according to Theorem 1,solving LMIs (6)leads to the following feasible solutions:

        Then=lnμ/α=0.364 6.And we can obtain that:‖xt‖≤2.075‖xt0‖.Let the initial state bex0=(-3 2)T,The simulation for the curves of the state is given in Fig.1.

        Fig.1 The curves of the state x(t)

        4 Conclusions

        In this paper,the exponential stability and robust exponential stability for switched system with multiple time-varing delays have been presented in terms of LMIs.Based on the average dwell time method,the sufficient conditions for the multiple time-varing delays has been obtained.Moreover,with a piecewise Lyapunov-Krasovskii functional proposed,we have obained a less conservative and more general results than the literature[16].And the effectivness of the proposed method has been verified by a simulation example.Finally,the state feedback problem is an open question.

        [1]BRANICKY M S.Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J].IEEE Trans on Autom Contr,1998,43(4):475-482.

        [2]LI Yan,LIU Yuzhong.Robust stabilization analysis for uncertain switched systems with time-varying delay[J].沈陽師范大學學報:自然科學版,2011,29(2):142-145.

        [3]DECARLO R A,BRANICKY M S.Perspective and results on stability and stabilization of hybrid systems[J].Proc IEEE,2000,88(7):1069-1082.

        [4]LIBERZON D,MORSE A S.Basic problems in stability and design of switched systems[J].IEEE Contr Syst Magazine,1999,19(5):59-70.

        [5]SHORTEN R N,NARENDRA K S.On the stability and existence of common Lyapunov functions for stable switching systems[C]∥Decision and Contr,1998:3723-3724.

        [6]SEHJEONG K,CAMPBELL S A,LIU X Z.Stability of a class of linear switching systems with time delay[J].IEEE Trans on Circuits and Syst-I,2006,53(2):384-393.

        [7]XIANG Zhengrong,WANG Ronghao.Robust stabilization of discrete-time switched non-linear systems with time delay under asynchronous switching[J].Trans Inst Measur Contr,2011,33(5):591-609.

        [8]MONDIE S E,KHARITONOV V L.Exponential estimates for retarded time-delay systems:an LMI approach[J].IEEE Trans on Autom Contr,2005,50(2):268-273.

        [9]LIEN C H,YU K W,LIN Y F,et al.Global exponential stability for uncertain delayed neural networks of neutral type with mixed time-delays[J].IEEE Trans Syst Man Cybern B,2008,38(3):709-720.

        [10]SUN Yuangong,WANG Long,XIE Guangming.Delay-dependent robust stability andH∞control for uncertain discrete-time switched systems with mode-dependent time delays[J].Appl Math Comput,2007,187(2):1228-1237.

        [11]ZHANG Wei,CAI Xiushan,HAN Zhengzhi.Robust stability criteria for systems with interval time-varying delay and nonlinear perturbations[J].J Comput Appl Math,2010,234(1):174-180.

        [12]ZHA Guisheng,SUN Ye,CHEN Xinkai,et al.Stability and L2gain analysis for switched symmetric systems with time-delay[C]∥Am Contr Conf,2003:2682-2687.

        [13]SUN Ximing,WANG Feng,LIU Guoping,et al.Stability analysis for linear switched systems with time-varying delay[J].IEEE Trans Syst Man Cybern B,2008,38(2):528 -533.

        [14]HIEN L V,HA Q P,PHAT V N.Stability and stabilization of switched linear dynamic systems with time delay and uncertainties[J].Appl Math Comput,2009,210(1):223-231.

        [15]ZHANG Xiaoli.Analysis of robust stability for switched systems with multiple time-delays[J].Contr Theor Appl,2011,9(2):283-288.

        [16]WANG Limin,SHAO Cheng.Robust stability analysis of switched uncertain systems with multiple time-varying delays and actuator failures[J].Contr Theor Appl,2011,9(2):267-272.

        [17]ZAIRONG Xi,GANG Feng.A switching algorithm for global expopnential stabilization of uncertain chained systems[J].IEEE Trans on Autom Contr,2003,48(10):1793-1798.

        猜你喜歡
        師范大學沈陽學報
        致敬學報40年
        沈陽分店
        藝術品(2019年9期)2019-10-26 06:42:14
        沈陽分店
        藝術品(2019年4期)2019-05-30 04:45:38
        Study on the harmony between human and nature in Walden
        長江叢刊(2018年8期)2018-11-14 23:56:26
        Balance of Trade Between China and India
        商情(2017年9期)2017-04-29 02:12:31
        Courses on National Pakistan culture in Honder College
        Film Music and its Effects in Film Appreciation
        學報簡介
        學報簡介
        LiteraryTechniquesEmployedtoDevelop Celie'sCharacterinThe Color Purple
        科技視界(2014年22期)2014-04-17 03:16:18
        国产亚洲日韩AV在线播放不卡| 久久久久99精品成人片欧美| 国产精品99精品久久免费| 亚洲97成人精品久久久| 免费国产自拍在线观看| 日韩吃奶摸下aa片免费观看| 色综合久久丁香婷婷| 国模无码视频专区一区| 日韩精品高清不卡一区二区三区| 亚洲乱码中文字幕视频| 夜夜揉揉日日人人青青| 精品国产高清a毛片无毒不卡 | 欧洲女人性开放免费网站| 精品国产香蕉伊思人在线又爽又黄| 日本黑人人妻一区二区水多多| 久久九九精品国产av| 精品少妇人妻av无码专区 | 国产精品女同久久久久久| 永久中文字幕av在线免费| 强开少妇嫩苞又嫩又紧九色| 日韩精品无码久久久久久 | 伊人久久亚洲综合影院首页| 精品国产污黄网站在线观看| 国产国产精品人在线视| 欧美激情a∨在线视频播放| 狠狠综合亚洲综合亚色| 亚洲第一女人的天堂av| 国产男女免费完整视频| 在线观看国产成人av片| 国产成人拍精品免费视频| 少妇性l交大片免费快色| 人妻熟妇乱又伦精品视频| 人妻少妇精品视频一区二区三区 | 久久无码潮喷a片无码高潮| 大香伊蕉国产av| 校花高潮一区日韩| 久久av不卡人妻出轨一区二区| 无人视频在线观看免费播放影院 | 91福利视频免费| 丰满人妻一区二区三区52| 亚洲精品在线免费视频|