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Planar Switched Systems

Author: NieWeiYang
Tutor: YangXiaoSong
School: Huazhong University of Science and Technology
Course: Operational Research and Cybernetics
Keywords: hybrid systems switched system stability closed orbit
Type: Master's thesis
Year: 2009
Downloads: 12
Quote: 0
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Hybrid systems have become one of the hottest issues in control theory, biology, computer science and other fields in recent years. Switched systems are relatively typical hybrid systems and they are also the most studied hybrid systems.The stability and trajectory of switched systems show us very amazing situation. For example, as described in the introduction, the two stable subsystems arise an unstable trajectory under a right switched law, and two unstable subsystems arise a stable trajectory under a right switched law. Even two-dimensional linear switched system can be a very complex situation. There is a lot of work need to be done.At present the study of switched systems focused on three aspects, the stability and stabilization of switched systems, the controllability of switched systems and the complexity dynamic behavior of switched systems. Most of the work concentrate on linear switched systems , and the nonlinear switched systems is a more difficult area.This article discusses the two-dimensional linear switched systems. Chapter III discusses two focus type subsystems arise a closed orbit under a right switched law, and points out the relationship of the parameters between two subsystems. Chapter IV discusses the sufficient conditions of stabilization at the neighborhood of origin of the two planar nonlinear switched systems. The detailed proof of the theorem and an example to verify the results of the preceding discussion is given out. Finally we point out that the above-mentioned switched law does not guarantee the overall stabilization of the switched systems, when the initial point is far away from the origin, the trajectory of switched system diverges to infinity..

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