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Exponential stability and robust exponential stability relating to switched systems consisting of stable and unstable nonlinear subsystems are considered in this study. At each switching time instant, the impulsive increments which are nonlinear functions of the states are extended from switched linear systems to switched nonlinear systems. Using the average dwell time method and piecewise Lyapunov function approach, when the total active time of unstable subsystems compared to the total active time of stable subsystems is less than a certain proportion, the exponential stability of the switched system is guaranteed. The switching law is designed which includes the average dwell time of the switched system. Switched systems with uncertainties are also studied. Sufficient conditions of the exponential stability and robust exponential stability are provided for switched nonlinear systems. Finally, simulations show the effectiveness of the result. 相似文献
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Inspired by the idea of multiple Lyapunov functions and the average dwell time, we address the stability analysis of nonautonomous continuous‐time switched systems. First, we investigate nonautonomous continuous‐time switched nonlinear systems and successively propose sufficient conditions for their (uniform) stability, global (uniform) asymptotic stability, and global (uniform) exponential stability, in which an indefinite scalar function is utilized to release the nonincreasing requirements of the classical multiple Lyapunov functions. Afterwards, by using multiple Lyapunov functions of quadratic form, we obtain the corresponding sufficient conditions for (uniform) stability, global (uniform) asymptotic stability, and global exponential stability of nonautonomous switched linear systems. Finally, we consider the computation issue of our current results for a special class of nonautonomous switched systems (ie, rational nonautonomous switched systems), associated with two illustrative examples. 相似文献
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Yansong Gao 《Asian journal of control》2013,15(5):1426-1433
This paper deals with the exponential stability and asynchronous stabilization of continuous‐time switched systems. By delicately constructed piecewise Lyapunov‐like functions and the minimum dwell time switching method, exponential stability of the switched systems with stable or unstable subsystems is obtained. Based on the result of the stability, the problem of controller design of the switched systems under asynchronous switching is also solved, and the delay that causes asynchronous phenomena can be unbounded. The stability results and control laws of the switched systems are formulated in the form of linear matrix inequalities that are numerically feasible. Finally, two illustrative numerical examples are presented to show the effectiveness of the obtained theoretical results. 相似文献
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In this paper, we aim to investigate the stability of 2D switched positive nonlinear systems with time‐varying delays in the Roesser model, which includes 2D switched positive linear systems as a special case. By using the average dwell time approach, we give a sufficient condition for the exponential stability of 2D switched positive nonlinear systems. The difficulty caused by the delays is overcome by introducing a model transform and the method used in this paper is different from conventional Lyapunov‐Krasovskii functional method. An explicit exponential bound on the decay rate is presented. We also extend the result to the general 2D switched linear systems, not necessarily positive. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result. 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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Xiaoli ZHANG 《控制理论与应用(英文版)》2011,9(2):283-288
The sufficient conditions of delay-dependent exponential stability for switched systems and robust exponential stability for uncertain switched systems with two time-delays are presented by using average dwell time method and free-weighting matrix method.The interaction between different time-delays is considered.The sufficient conditions do not need that every subsystem is stable.The designed methods of the switching law are also given.The sufficient conditions are given in the form of linear matrix inequalities that can be solved easily.The result is proven to be valid by the simulation at last. 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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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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本文通过利用平均驻留时间方法,研究一类具有不确定性非线性切换时延系统的指数稳定性问题。给出非切换系统的候选李雅普诺夫函数的衰减估计分析,然后以线性矩阵不等式的形式给出使系统保持指数稳定及鲁棒指数稳定的充分条件,同时也给出了系统状态指数衰减的具体的估计形式。 相似文献
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本文研究了具有无穷时滞切换不确定细胞神经网络(UCNNs)系统任意切换下的指数稳定性.利用同胚映射和M-矩阵理论,得到UCNNs系统平衡点存在性,唯一性和指数稳定性的充分条件;利用Lyapunov泛函方法,研究了时滞切换UCNNs系统任意切换下的鲁棒指数稳定性,并得到确保系统全局指数稳定的充分条件. 相似文献
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This paper is concerned with the problems of absolute exponential stability and stabilization for a class of switched nonlinear systems whose system matrices are Metzler. Nonlinearity of the systems is constrained in a sector field, which is bounded by two odd symmetric piecewise linear functions. Multiple Lyapunov functions are introduced to deal with the stability of such nonlinear systems. Compared with some existing results obtained by the common Lyapunov function approach in the literature, the conservatism of our results is reduced. All present conditions can be solved by linear programming. Furthermore, the absolute exponential stabilization for the considered systems is designed by the state-feedback and average dwell time switching strategy. Two examples are also given to illustrate the validity of the theoretical findings. 相似文献
13.
Ji-Shi Zhang Jiang-Wen Xiao Yan-Jun Shen 《International journal of systems science》2014,45(12):2458-2465
This paper addresses the stability problem of switched positive linear systems with stable and unstable subsystems. Based on a multiple linear copositive Lyapunov function, and by using the average dwell time approach, some sufficient stability criteria of global uniform exponential stability are established in both the continuous-time and the discrete-time cases, respectively. Finally, some numerical examples are given to show the effectiveness of the proposed results. 相似文献
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Minimum Dwell Time for Global Exponential Stability of a Class of Switched Positive Nonlinear Systems
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This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler. A class of multiple time-varying Lyapunov functions is constructed to obtain the computable sufficient conditions on the stability of such switched nonlinear systems within the framework of minimum dwell time switching. All present conditions can be solved by linear/nonlinear programming techniques. An example is provided to demonstrate the effectiveness of the proposed result. 相似文献
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一类受扰动脉冲切换系统鲁棒指数镇定 总被引:3,自引:1,他引:2
提出一类具有边界范数有界扰动的脉冲切换系统在任意切换条件下鲁棒指数镇定问题。应用Lyapunow直接法,导出这类受扰动脉冲切换系统指数稳定的充分条件并且给出线性时不变状态反馈控制律使该受扰动脉冲切换系统指数镇定,最后,给出数值示例说明所得到的结果是有效的。 相似文献
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The exponential stability of a class of switched systems containing stable and unstable subsystems with impulsive effect is analyzed by using the matrix measure concept and the average dwell- time approach. It is shown that if appropriately a large amount of the average dwell- time and the ratio of the total activation time of the subsystems with negative matrix measure to the total activation time of the subsystems with nonnegative matrix measure is chosen , the exponential stability of a desired degree is guaranteed. Using the proposed switching scheme ,we studied the robust exponential stability for a class of switched systems with impulsive effect and structure perturbations. Simulations validate the main results. 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
20.
The exponential stability of a class of switched systems containing stable and unstable subsystems with impulsive effect is analyzed by using the matrix measure concept and the average dwell-time approach. It is shown that if appropriately a large amount of the average dwell-time and the ratio of the total activation time of the subsystems with negative matrix measure to the total activation time of the subsystems with nonnegative matrix measure is chosen, the exponential stability of a desired degree is guaranteed. Using the proposed switching scheme, we studied the robust exponential stability for a class of switched systems with impulsive effect and structure perturbations. Simulations validate the main results. 相似文献