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Unified dwell time–based stability and stabilization criteria for switched linear stochastic systems and their application to intermittent control 下载免费PDF全文
This paper considers the stability and stabilization problems for the switched linear stochastic systems under dwell time constraints, where the considered systems can be composed of an arbitrary combination of stable and unstable subsystems. First, a time‐varying discretized Lyapunov function is constructed based on the projection of a linear Lagrange interpolant and a switching‐time‐dependent “weighted” function. The “weighted” function not only enforces the Lyapunov function to decrease at switching instants but also coordinates the dynamical behavior of the subsystems. As a result, some unified criteria for mean square stability and almost sure stability of the switched stochastic systems are established in terms of linear matrix inequalities. Based on the obtained stochastic stability criteria, 2 types of state feedback controllers for the systems are designed. Moreover, the novel results are applied to solve the intermittent control or the controller failure problems. Finally, conservatism analysis and numerical examples are provided to illustrate the effectiveness of the established theoretical results. 相似文献
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In this study, we investigate the stochastic input-to-state stability (SISS) of impulsive switched stochastic nonlinear systems. In this model, the impulse jumps are component multiple maps that depend on time. Thus the model differs from traditional impulsive systems with single impulse between two adjacent switching times. We provide sufficient conditions in three cases with the SISS system by using the Lyapunov function and average impulsive interval approach. The destabilising impulses cannot destroy the SISS properties if the impulses do not occur too frequently when all the subsystems that control the continuous dynamics are SISS. In other words, the average impulsive interval satisfies a lower bound restraint. Conversely, when all subsystems that control the continuous dynamics are not SISS, impulses can contribute to stabilising the system in the SISS sense when the average impulsive interval satisfies an upper bound. Then, we investigate the SISS property of impulsive switched stochastic nonlinear systems with some subsystems that are not SISS under certain conditions such that the property remains obtained. Finally, we show three examples to demonstrate the validity of the main result. 相似文献
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ABSTRACTThis paper addresses the finite-time stability problem of linear switched singular systems with finite-time unstable subsystems. Dynamic decomposition techniques are used to transform such systems into equivalent one that is a reduced-order switched normal systems. Based on the mode-dependent average dwell time (MDADT) switching signal, new sufficient conditions are presented to guarantee the linear switched singular systems with finite-time unstable subsystems being finite-time stability, finite-time bounded and finite-time stabilization. Finally, a numerical example is employed to verify the efficiency of the preceding method. 相似文献
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This paper investigates almost sure exponential stability and feedback stabilization for switched time‐delay systems with nonlinear stochastic perturbations. The main contributions of this paper are threefold: (i) based on the non‐convolution type multiple Lyapunov functionals and the mathematical induction approach, a mean‐square exponential stability condition for nonlinear stochastic switched systems is first established, such that the obtained average dwell time does not rely on any given decay rate; (ii) by using the method developed in part (i) and the stochastic analysis techniques and limit methods in probability, an almost sure exponential stability criterion for switched delayed systems with nonlinear stochastic uncertainties is presented, and then a state feedback controller for the systems under consideration is designed; and (iii) when certain assumptions are made on the nonlinear stochastic perturbations, the results in this paper are further improved by relaxing some conditions. The effectiveness of the proposed method is demonstrated by three illustrative examples. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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研究异步切换下时滞切换正系统的有限时间控制问题,即针对控制器切换滞后于子系统切换形成的异步现象,基于平均驻留时间切换方法对切换正系统开展有限时间镇定研究.首先,将每个正子系统运行的区间划分为子系统与控制器匹配和失配区间,并构造多余正Lyapunov-Krasovskii泛函;其次,基于有限时间稳定理论,实现平均驻留时间切换律及异步时滞切换正系统有限时间镇定控制器的联合设计,并给出连续时间和离散时间两种情形下系统有限时间镇定的充分条件;最后,通过两个仿真例子验证所提出方法的有效性. 相似文献
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In this paper, we investigate the stability analysis problem of switched impulsive nonlinear systems and several stabilization problems of switched discrete‐time linear systems are studied. First, sufficient conditions ensuring globally uniformly asymptotically stability of switched nonlinear impulsive system under arbitrary and DDT (dynamical dwell time which defines the length of the time interval between two successive switchings) switching are derived, respectively. In the DDT switching case, we first consider the switched system composed by stable subsystems, then we extend the results to the case where not all subsystems are stable. The stabilizations of switched discrete‐time linear system under arbitrary switching, DDT switching and asynchronous switching are investigated respectively. Based on the stability analysis results, the control synthesis consists of controller design for each subsystem and state impulsive jumping generators design at switching instant. With the aid of the state impulsive jumping generators at switching instant, the ‘energy’ produced by switching can be minimized, which leads to less conservative results. Several numerical examples are given to illustrate the proposed results within this paper. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Stability and Stabilization of Two‐Dimensional LTI Switched Systems with Potentially Unstable Focus 下载免费PDF全文
Liying Zhu 《Asian journal of control》2015,17(3):892-907
This paper investigates stability and stabilization of two‐dimensional switched linear time‐invariant (LTI) systems with potentially unstable focus. For the case that the origin is a single common focus of all subsystems, we first give continuous positive definite functions related only to the elements of subsystems' state matrices. Then, based on the continuous positive definite functions obtained, this paper proposes several sufficient conditions of stability/asymptotic stability/instability of the kind of switched LTI systems. By means of the stability results proposed, global asymptotic stabilizing controls (GASC), global asymptotic stabilizing switching paths (GASSP) and corresponding algorithms are designed for two‐dimensional switched LTI systems with focus. Finally, two illustrative examples and numerical simulations demonstrate the effectiveness of the new stability and stabilization results obtained in this paper. 相似文献
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Qunxian Zheng Hongbin Zhang Dianhao Zheng 《International Journal of Control, Automation and Systems》2017,15(3):986-994
The stability analysis and asynchronous stabilization problems for a class of discrete-time switched nonlinear systems with stable and unstable subsystems are investigated in this paper. The Takagi-Sugeno (T-S) fuzzy model is used to represent each nonlinear subsystem. Through using the T-S fuzzy model, the studied systems are modeled into the switched T-S fuzzy systems. By using the switching fuzzy-basis-dependent Lyapunov functions (FLFs) approach and mode-dependent average dwell time (MDADT) technique, the stability conditions for the open-loop switched T-S fuzzy systems with unstable subsystems and asynchronous stabilization conditions for the closed-loop switched T-S fuzzy systems with unstable subsystems are obtained. Both the stability results and asynchronous stabilization results are derived in terms of linear matrix inequalities (LMIs). Finally two numerical examples are provided to illustrate the effectiveness of the results obtained. 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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The stability problem of switched delay systems with all subsystems unstable is investigated in this paper. A sufficient criterion is firstly proposed to guarantee asymptomatic stability of nonlinear switched delay systems with all subsystems unstable, where the stabilization property of switching behaviors is exploited to compensate the divergence of states. Then by constructing multiple discretized Lyapunov-Krasovskii functionals, stability criteria are developed for linear switched time-invariant and time-varying delay systems with all subsystems unstable. Finally, two examples are provided to illustrate the feasibility, superiority and application of the proposed approach. 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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Stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems. In this brief paper, a sufficient condition ensuring the asymptotic stability of switched continuous-time systems with all modes unstable is proposed. The main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes. Then, by using a discretized Lyapunov function approach, a computable sufficient condition for switched linear systems is proposed in the framework of dwell time; it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability. Based on derived results, an algorithm is proposed to compute the stability region of admissible dwell time. A numerical example is proposed to illustrate our approach. 相似文献
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This paper studies the stability and stabilization problems for a class of switched stochastic systems under asynchronous switching. The asynchronous switching refers to that the switching of the candidate controllers does not coincide with the switching of system modes. Two situations are considered: (1) time-delayed switching situation, that is, the switching of the candidate controllers has a lag to the switching of the system modes; (2) mismatched switching situation, the switching of the candidate controllers does not match the switching of the system modes. Using average dwell time and Lyapunov-like function, sufficient conditions are established for stochastic input-to-state stability of the whole system. Also, the stabilizing controller design approach is proposed for switched stochastic linear systems. The minimal average dwell time and the controller gain are achieved. Finally, a numerical example is used to demonstrate the validity of the developed results. 相似文献
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Mei Xiang Zhengrong Xiang Hamid Reza Karimi 《International Journal of Control, Automation and Systems》2014,12(5):939-947
This paper investigates the state feedback stabilization problem for a class of positive switched systems with time-varying delays under asynchronous switching in the frameworks of continuous-time and discrete-time dynamics. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. By constructing an appropriate co-positive type Lyapunov-Krasovskii functional and further allowing the functional to increase during the running time of active subsystems, sufficient conditions are provided to guarantee the exponential stability of the resulting closed-loop systems, and the corresponding controller gain matrices and admissible switching signals are presented. Finally, two illustrative examples are given to show the effectiveness of the proposed methods. 相似文献
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《Automatic Control, IEEE Transactions on》2008,53(9):2149-2153
Characterization and control of stability of switched dynamical systems and differential inclusions have attracted significant attention in the recent past. The most of the current results for this problem are obtained by application of the Lyapunov function method which provides sufficient but frequently over conservative stability conditions. For planar systems, practically verifiable necessary and sufficient conditions are found only for switched systems with two subsystems. This paper provides explicit necessary and sufficient conditions for asymptotic stability of switched systems and differential inclusions with arbitrary number of subsystems; these conditions turned out to be identical for the both classes of systems. A precise upper bound for the number of switching points in a periodic solution, corresponding to the break of stability, is found. It is shown that, for a switched system, the break of stability may also occur on a solution with infinitely fast switching (chattering) between some two subsystems. 相似文献
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针对一类切换线性系统,本文提出了一种基于系统状态的驻留时间策略.这种切换策略不仅使异步状态反馈切换系统稳定,而且缩短了系统的运行时间.对于异步切换系统的稳定性和增益问题,本文主要的结论是在子系统运行期间Lyapunov函数允许增加,同时又没有的限制.通过利用基于系统状态的驻留时间策略,推导出了切换线性系统的控制器设计的充分条件.得出的结论也可以推广到非线性切换系统.本文中最后给出的算例用于说明该方法的有效性. 相似文献