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The concepts of semistability and exponential semistability are well-developed for finite-dimensional systems with nonisolated equilibrium points, where asymptotic or exponential stability is not possible. Definitions of semistability and exponential semistability have recently been formulated for networks with time-delays. This paper further extends the semistability theory to continuous and discrete spatially distributed systems. This requires the definition of the notions of exact and approximate semicontrollability and semiobservability, and discrete approximate semicontrollability and semiobservability. Also introduced is the property of weak semistability. Necessary and sufficient conditions are given for exponential semistability and weak semistability, and sufficient conditions are given for semistability. 相似文献
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Iman Zamani Masoud Shafiee Asier Ibeas 《International journal of systems science》2014,45(5):1128-1144
The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities (LMIs). By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method. 相似文献
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ABSTRACTThis paper is devoted to study the stability of switched singular stochastic linear systems with both stable and unstable subsystems. By using the method of multiple Lyapunov functions and the notion of average dwell time, we provide sufficient conditions for the exponential mean-square stability of switched singular stochastic systems in terms of a proper switching rule and the linear matrix inequalities. An example is given to illustrate the effectiveness of the obtained results. 相似文献
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This paper presents the exponential stability of output‐based event‐triggered control for switched singular systems. An event‐triggered mechanism is introduced based on measure output, by employing the Lyapunov functional method and average dwell time approach, some sufficient conditions for exponential stability of the switched singular closed‐loop systems are derived. Furthermore, dynamic output feedback controller parameters are obtained. Lastly, a numerical example is given to illustrate the validity of the proposed solutions. 相似文献
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分布参数切换系统的稳定性分析 总被引:3,自引:0,他引:3
将切换系统的概念引入到分布参数系统中,提出分布参数切换系统的概念.结合切换系统和分布参数系统的建模方法,建立了两类分布参数切换系统的模型.运用切换系统的稳定性分析方法,对两类分布参数切换系统的稳定性进行分析,得出了指数稳定的充分条件.仿真示例验证了定理的正确性. 相似文献
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This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are derived in terms of linear matrix inequalities and average dwell-time conditions. Numerical examples are also given to illustrate the results. 相似文献
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本文研究了在拒绝服务攻击下网络化非线性系统的采样数据输出反馈控制问题.首先,为了避免使用完整的状态信息,在存在拒绝服务攻击的情况下设计了一种新颖的切换观测器.其次,同时考虑两个采样周期和拒绝服务攻击的影响,建立了一个新的切换增广系统模型,包括系统本身和误差系统.利用该模型和分段Lyapunov-Krasovskii泛函方法推导出保证切换增广系统是指数稳定的充分条件.进一步,利用线性矩阵不等式的解给出了观测器和控制器增益的共同设计方案.最后,通过仿真验证所提出控制方法的有效性. 相似文献
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《Automatic Control, IEEE Transactions on》2006,51(9):1536-1541
This note develops sufficient conditions for exponential convergence of resetting hybrid nonlinear dynamical systems. Using nonlinear contraction theory, the analysis first develops a unified formulation of continuous-time and discrete-time nonlinear dynamics based on a differential transition matrix. This yields enhanced dwell-time based conditions for stability of such systems analogous to those existing for switched systems. It turns out that such dwell-time based conditions, unlike their counterparts for switched systems, include arbitrary stability conditions as a special case, and are less conservative and much simpler to verify. 相似文献
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The issue of exponential stability analysis of continuous‐time switched singular systems consisting of a family of stable and unstable subsystems with time‐varying delay is investigated in this paper. It is very difficult to analyze the stability of such systems because of the existence of time‐delay and unstable subsystems. In this regard, on the basis of the free‐weighting matrix approach, by constructing the new Lyapunov‐like Krasovskii functional, and using the average dwell‐time approach, delay‐dependent sufficient conditions are derived and formulated in terms of LMIs to check the exponential stability of such systems. This paper also highlights the relationship between the average dwell‐time of the switched singular time‐delay system, its stability, exponential convergence rate of differential states, and algebraic states. Finally, a numerical example is given to confirm the analytical results and illustrate the effectiveness of the proposed strategy. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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In this paper, the mean square (MS) stability and exponential mean square (EMS) stability of multi-variable switched stochastic systems are investigated. Based on the concept of the average dwell-time and the ratio of the total time running on all unstable subsystems to the total time running on all stable subsystems, some sufficient conditions are given to ensure the MS stability and EMS stability of the switched stochastic systems involved. Further, for the switched stochastic control systems with all subsystems controllable or stabilizable, EMS stabilization controls and sufficient conditions on EMS stabilization are presented, and the convergent rates of the closed-loop systems are obtained. 相似文献
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不确定时滞Lur''''e型控制系统与时滞相关的绝对稳定性(英文) 总被引:1,自引:0,他引:1
研究了一类参数不确定的具有多个时滞的Lur'e型控制系统与时滞相关绝对稳定性问题.通过将原系统变换为等价的奇异系统,利用Moon不等式放大向量积,构造出一个新的Lya-punov-Krasovskii泛函.并由此基于线性矩阵不等式,得到了系统与时滞相关绝对稳定的充分条件.这些充分条件无须预调任何参数矩阵,可以直接运用Matlab软件中LMI工具箱求解.数值例子表明,与现有结果相比,本文结果较大地改进了保证不确定时滞Lur'e型控制系统绝对稳定的时滞界. 相似文献
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This paper deals with the problems of passivity and passification for a class of discrete‐time switched stochastic systems with time‐varying delay. Based on the average dwell time approach, the piecewise Lyapunov function technique, and the free‐weighting matrix method, a new Lyapunov functional is proposed and sufficient conditions for mean‐square exponential stability and stochastic passivity are developed under average dwell time switching. Moreover, an estimate of state decay can be calculated in terms of linear matrix inequalities (LMIs). Then, the solvability condition for passification is established and the corresponding controller is designed. Two numerical examples are given to show the effectiveness of the proposed methods. 相似文献
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研究同时存在双通道数据包丢失和时变时延的Delta算子网络控制系统(NCSs)故障检测问题.假定数据包丢失发生在控制器到执行器、传感器至控制器的数据传输过程中,并且利用两个相互独立的伯努利随机变量描述是否发生丢包.将上述的NCSs建模为网络切换系统,提出任意切换律下故障检测滤波器的设计方法.利用线性矩阵不等式(LMIs)方法、Lyapunov-Krasovskii泛函和平均驻留时间等得出所考虑的网络切换系统具备指数均方稳定性的充分条件.证明了所用的网络切换系统满足H∞性能,并推导出了滤波器参数的显式表达.数值仿真结果验证了所提方法的有效性. 相似文献
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Qiang Yu 《International journal of systems science》2013,44(7):1278-1287
The problem of robust stability for switched linear systems with all the subsystems being unstable is investigated. Unlike the most existing results in which each switching mode in the system is asymptotically stable, the subsystems may be unstable in this paper. A necessary condition of stability for switched linear systems is first obtained with certain hypothesis. Then, under two assumptions, sufficient conditions of exponential stability for both deterministic and uncertain switched linear systems are presented by using the invariant subspace theory and average dwell time method. Moreover, we further develop multiple Lyapunov functions and propose a method for constructing multiple Lyapunov functions for the considered switched linear systems with certain switching law. Several examples are included to show the effectiveness of the theoretical findings. 相似文献
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This paper studies the exponential stability problems of discrete‐time and continuous‐time impulsive positive switched systems with mixed (discrete and distributed) time‐varying delays, respectively. By constructing novel copositive Lyapunov‐Krasovskii functionals and using the average dwell time technique, delay‐dependent sufficient conditions for the solvability of considered problems are given in terms of fairly simple linear matrix inequalities. Compared with the most existing results, by introducing an extra real vector, restrictive conditions on derivative of the time‐varying delays (less than 1) are relaxed, thus the obtained improved stability criteria can deal with a wider class of continuous‐time positive switched systems with time‐varying delays. Finally, two simple examples are provided to verify the validity of theoretical results. 相似文献