Reachability realization and stabilizability of switched linear discrete-time systems |
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Authors: | Guangming Xie Long Wang |
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Institution: | Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China |
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Abstract: | In this paper, the reachability realization of a switched linear discrete-time system, which is a collection of linear time-invariant discrete-time systems along with some maps for “switching” among them, is addressed. The main contribution of this paper is to prove that for a switched linear discrete-time system, there exists a basic switching sequence such that the reachable (controllable) state set of this basic switching sequence is equal to the reachable (controllable) state set of the system. Hence, the reachability (controllability) can be realized by using only one switching sequence. We also discuss the stabilizability of switched systems, and obtain a sufficient condition for stabilizability. Two numeric examples are given to illustrate the results. |
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Keywords: | Switched linear discrete-time system Switching sequence Reachable state set Reachability realization Controllable state set Controllability realization Stabilizability |
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