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This paper explores the relations between asymptotic stability and exponential stability of continuous-time and discrete-time positive systems with delay. A system is said to be positive if its state and output are non-negative whenever the initial condition and input are non-negative. Two results are obtained. First, if a positive system is asymptotically stable for all bounded (further continuous, for continuous-time systems) time-varying delays, then it is exponentially stable for all such delays. In particular, if a positive system is asymptotically stable for a given constant delay, then it is exponentially stable for all constant delays. Second, if the involved delays are unbounded, then the positive system may be not exponentially stable even if it is asymptotically stable. 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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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
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In this paper, a class of impulsive stochastic switched systems with mixed delays is considered. On the basis of some integro-differential inequalities and stochastic analysis techniques, some general criteria for mean square exponential stability are obtained. An example is given to illustrate the theory. 相似文献
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This article studies the stability problem of discrete-time positive switched linear systems by introducing a nonzero elements chain method. Compared to existing works, the highlight of this article is reflected in the inclusiveness of the subsystem, that is, each subsystem is allowed to be stable, marginally stable or even unstable. Some sufficient conditions depending on the characteristics of system matrices and the time-dependent switching signals are established, so as to guarantee the exponential stability of positive switched linear systems. In addition, the main result is extended to the case of time-varying delay. At last, the superiority of the obtained results is well verified by numerical examples. 相似文献
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In this paper, we present an extension of the concept of componentwise asymptotic (exponential) stability of linear systems in the non-symmetrical case. The main motivation for these results is the need for a more detailed evaluation of the dynamical behaviour of linear systems in electrical engineering and biology. Necessary and sufficient conditions for componentwise asymptotic (exponential) stability in the non-symmetrical case are given. The symmetrical case is obtained as a particular case. © 1997 by John Wiley & Sons, Ltd. 相似文献
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This paper addresses the links between three stabilities (attractivity, asymptotic stability, and exponential stability) of switched homogeneous systems with delays and uncertainties. A system has a certain property over a given set of switching signals if the property holds for all switching signals in . It is shown that a switched homogeneous system of degree one is exponentially stable over a given set of switching signals if it is attractive or asymptotically stable over the same set. The result is then applied to switched linear systems with delays and uncertainties. Finally, an example follows to show that ‘being over a given set of switching signals’ is necessary to guarantee the equivalence between different stabilities. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Tai-Fang Li Georgi M. Dimirovski Yanyan Liu 《International journal of systems science》2013,44(6):1076-1088
This article is concerned with the stability analysis for a class of switched neutral systems with mixed time-varying delays. The upper bound of derivative of the discrete time-varying delay is not restricted to one. A delay-dependent criterion of exponential stability under switching signals with an average dwell time is developed by employing free weighting matrices. The criterion is given in the form of linear matrix inequality. A state decay estimation for the switched system is explicitly given by considering the individual rate of decay of state for each subsystem. Two simulation examples are given to illustrate the effectiveness of the proposed method. 相似文献
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在非均匀采样系统中,存在着刷新时间间隔不确定、时变的情况,这给系统控制器的设计造成了很大困难.为此,将刷新时间间隔看作时延变量,不同时延大小情况下的系统动态变化用不同子系统模型刻画,从而将时延的变化律转化为不同子模型之间的切换律,将非均匀采样系统描述为一类具有有限个子系统的离散时间切换系统.通过定理形式给出含有不确定刷新时间间隔的反馈闭环系统鲁棒稳定性的充分条件. 相似文献
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提出一类新型的切换模糊系统,即以聚类型模糊集合为基础的切换模糊系统.模糊模型的前件采用聚类型模糊集合和隶属度函数的形式.在研究中,首先讨论聚类型模糊集合的切换模糊系统形式和机理;然后,使用多Lyapunov函数给出离散切换模糊系统在满足最小驻留时间切换策略下的指数稳定性条件,并设计出切换律;最后,通过仿真实例验证所提出方法的有效性. 相似文献
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Rifat Sipahi Nejat Olgac Dimitri Breda 《International journal of systems science》2013,44(12):1445-1455
First-order linear time invariant and time-delayed dynamics of neutral type is taken into account with three rationally independent delays. There are two main contributions of this study. (a) It is the first complete treatment in the literature on the stability analysis of systems with three delays. We use a recent procedure, the cluster treatment of characteristic roots (CTCR), for this purpose. This procedure results in an exact and exhaustive stability tableau in the domain of the three delays. (b) It provides a proof of a complex concept called the delay-stabilisability (also known as strong stability) as a by-product of CTCR. Furthermore, we deploy a numerical method (infinitesimal generator approach) to approximate the dominant characteristic roots of this class of systems, which concur with the stability outlook generated by CTCR. 相似文献
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This paper is concerned with event-triggered control for the switched system with time-varying delay and dynamic input quantization. The work is aimed at solving the quantizer saturation in the finite-level quantized control design and the mismatch caused by event-triggered sampling and the switching. First of all, the quantization parameter updating laws are designed respectively in the case of match and mismatch between the system and the controller under the event-triggered mechanism without Zeno behavior. Then, the total variation of Lyapunov functional is transformed into discrete time updating of the dynamic quantization parameter. A switching law and a quantized control strategy are developed to ensure the exponential stability of switched systems with delay and input quantization. At last, two examples are given to illustrate the validity of the results. 相似文献