On the static output feedback stabilisation of discrete event dynamic systems based upon the approach of semi-tensor product of matrices |
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Authors: | Zhipeng Zhang Xiaoguang Han Zhongxin Liu |
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Affiliation: | 1. School of Computer Science and Engineering, Tianjin University of Technology, Tianjin, People's Republic of China;2. College of Artificial Intelligence, Nankai University, Tianjin, People's Republic of China;3. College of Electronic Information and Automation, Tianjin University of Science and Technology, Tianjin, People's Republic of China;4. College of Artificial Intelligence, Nankai University, Tianjin, People's Republic of China |
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Abstract: | In this paper, the static output feedback stabilisation of discrete event dynamic systems (DEDSs) is investigated via the semi-tensor product (STP) of matrices. Firstly, the dynamics of DEDSs modelled by deterministic Moore-type finite automata are converted into an matrix expression in the STP frame. Secondly, necessary and sufficient conditions for the existence of a static output feedback control pattern, stabilising the controlled discrete event dynamic systems to some equilibrium point, are given, and constructive algorithms to seek the static output feedback control pattern including an effective specific solution algorithm and an analytic solution algorithm are proposed. Thirdly, the equilibrium-based static output feedback stabilisation of DEDSs is extended to the set-based static output feedback stabilisation and necessary and sufficient conditions and constructive algorithms to seek the corresponding control pattern are provided. Finally, some examples are presented to illustrate the effectiveness of the proposed approach. |
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Keywords: | Discrete event dynamic systems semi-tensor product of matrices finite automata Moore automata static output feedback stabilisation |
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