Matrix approach to detectability of discrete event systems |
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| Institution: | 1. School of Mathematics, Shandong University, Jinan, Shandong 250100, PR China;2. School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore;1. School of Mathematics, Shandong University, Jinan 250100, China;2. College of Information Engineering, Henan University of Science and Technology, Luoyang 471000, China |
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| Abstract: | This paper studies the detectability problem of discrete event systems (DESs), and devotes to providing a synthetical method to cope with multiple cases, including (partial) event observation and/or partial state observation. By using the semi-tensor product method, two equivalent types of algebraic expressions are presented for DESs, based on which reachability of DESs is investigated in detail and a new tool called detection matrix is defined. Then, four matrix-based necessary and sufficient conditions are derived for checking different kinds of detectability. Finally, for better presentation, two examples are shown to demonstrate that the theoretical results are efficient. |
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