共查询到10条相似文献,搜索用时 156 毫秒
1.
Alexander Aleksandrov Elena Aleksandrova Alexei Zhabko 《International journal of systems science》2017,48(10):2111-2119
Stability of certain classes of nonlinear time-delay switched systems is studied. For the corresponding families of subsystems, conditions of the existence of common Lyapunov–Razumikhin functions are found. The fulfilment of these conditions provides the asymptotic stability of the zero solutions of the considered hybrid systems for any switching law and for any nonnegative delay. Some examples are presented to demonstrate the effectiveness of the obtained results. 相似文献
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In this paper we derive necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for a finite set of linear positive systems. Both the state dependent and arbitrary switching cases are considered. Our results reveal an interesting characterisation of “linear” stability for the arbitrary switching case; namely, the existence of such a linear Lyapunov function can be related to the requirement that a number of extreme systems are Metzler and Hurwitz stable. Examples are given to illustrate the implications of our results. 相似文献
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The stability of the trivial solution for a class of difference systems with switching and sector-type nonlinearities is studied. Different approaches to common Lyapunov function design for the family of subsystems corresponding to the considered switched system are proposed. Sufficient conditions making the trivial solution asymptotically stable for any switching law are determined. In the case when common Lyapunov function design fails, multiple Lyapunov functions are used to obtain the restrictions on the switching law guaranteeing the asymptotic stability of the trivial solution. 相似文献
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In this paper we consider the asymptotic stability of a class of discrete-time switching linear systems, where each of the constituent subsystems is Schur stable. We first present an example to motivate our study, which illustrates that the bilinear transform does not preserve the stability of a class of switched linear systems. Consequently, continuous time stability results cannot be transformed to discrete time analogs using this transformation. We then present a subclass of discrete-time switching systems that arise frequently in practical applications. We prove that global attractivity for this subclass can be obtained without requiring the existence of a common quadratic Lyapunov function (CQLF). Using this result, we present a synthesis procedure to construct switching stabilizing controllers for an automotive control problem, which is related to the stabilization of a vehicle’s roll dynamics subject to switches in the center of gravitys (CG) height. 相似文献
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具有块三角结构非线性切换系统的二次稳定性 总被引:6,自引:0,他引:6
The problem of globally quadratic stability of switched nonlinear systems in block-triangular form under arbitrary switching is addressed. Under the assumption that all block-subsystems are zero input-to-state stable, a sufficient condition for the problem to be solvable is presented. A common Lyapunov function is constructed iteratively by using the Lyapunov functions of block-subsystems. 相似文献
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Studies the global asymptotic stability of a class of fuzzy systems. It demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant (LTI) switching systems. A necessary and sufficient condition for the stability of such systems are given, and it is shown that under the sufficient condition, a common Lyapunov function exists for the LTI subsystems. A particular case when the system matrices can be simultaneously transformed to normal matrices is shown to correspond to the existence of a common quadratic Lyapunov function. A constructive procedure to check the possibility of simultaneous transformation to normal matrices is provided 相似文献
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The theory of H ∞ control of switched systems is extended to stochastic systems with state‐multiplicative noise. Sufficient conditions are obtained for the mean square stability of these systems where dwell time constraint is imposed on the switching. Both nominal and uncertain polytopic systems are considered. A Lyapunov function, in a quadratic form, is assigned to each subsystem that is nonincreasing at the switching instants. During the dwell time, this function varies piecewise linearly in time following the last switch, and it becomes time invariant afterwards. Asymptotic stochastic stability of the set of subsystems is thus ensured by requiring the expected value of the infinitesimal generator of this function to be negative between switchings, resulting in conditions for stability in the form of LMIs. These conditions are extended to the case where the subsystems encounter polytopic‐type parameter uncertainties. The method proposed is applied to the problem of finding an upper bound on the stochastic L2‐gain of the system. A solution to the robust state‐feedback control problem is then derived, which is based on a modification of the L2‐gain bound result. Two examples are given that demonstrate the applicability of the proposed theory. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
9.
Robust Output Feedback Stabilization of Switched Nonlinear Systems with Average Dwell Time 下载免费PDF全文
Li‐Chen Fu 《Asian journal of control》2014,16(1):264-276
For some switched nonlinear systems, stabilization can be achieved under arbitrary switching with state feedback control. Due to switching zero dynamics, output feedback stabilization for some switched nonlinear systems needs dwell time between switching to guarantee system stability. In this paper, we consider a class of switched nonlinear systems with unknown parameters and unknown switching signals. We design a robust output feedback controller that stabilizes the system under a class of switching signals with average dwell time (ADT) where the value of ADT can be reduced by adjusting the control gain. For some special cases, common quadratic Lyapunov functions of the closed‐loop systems can be found and the value of ADT is further relaxed. Some examples and simulations are provided to validate the results. 相似文献
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Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching 总被引:1,自引:0,他引:1
Zhao-Jing Wu Author Vitae Xue-Jun Xie Author Vitae Peng Shi Author Vitae Yuan-qing Xia Author Vitae 《Automatica》2009,45(4):997-1004
A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case. 相似文献