Robust convergence of discrete‐time delayed switched nonlinear systems and its applications to cascade systems |
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Authors: | Xingwen Liu Qianchuan Zhao |
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Affiliation: | 1. College of Electrical and Information Engineering, Southwest University for Nationalities, Chengdu 610041, China;2. Center for Intelligent and Networked Systems, Department of Automation, and TNList, Tsinghua University, Beijing 100084, China |
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Abstract: | Systems in real world are always subject to perturbations. This paper addresses the convergence properties of a class of nominal systems with perturbations. It is assumed that the nominal system is a switched nonlinear exponentially stable one with time‐varying delays and that the perturbation exponentially or asymptotically converges to zero. It is revealed that the trajectories of the perturbed system behave as the perturbation, ie, trajectories exponentially or asymptotically converge to zero, depending on the property of perturbation. Applying these results to cascade switched nonlinear systems, it is shown that such systems are exponentially stable if and only if all the subsystems, obtained by removing the coupling terms, are exponentially stable. A similar conclusion is presented for systems being asymptotically stable. Finally, a numerical example illustrates the proposed theoretical results. |
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Keywords: | asymptotic stability cascade systems delays exponential stability switched systems |
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