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I-Detectability of Networked Discrete Event Systems by Matrix Approach

Kexin Ren, Zhipeng Zhang*, and Chengyi Xia*
International Journal of Control, Automation, and Systems, vol. 20, no. 3, pp.750-757, 2022

Abstract : State estimation is the primary concern in system analysis and control issues, especially for complex networked systems. This paper explores the influence of communication delays on the initial-state detectability of networked discrete event systems (NDESs). Firstly, the communication delays are hypothesized to be upper bounded through the observation channel, and the notion of networked initial-state (NI) detectability is proposed and lucubrated. Subsequently, according to the semi-tensor product (STP) of matrices, the dynamics affected by bounded delays could be perfectly depicted by a reachable matrix. Then, these algebraic criteria of NI detectability: strongly NI and weakly NI detectability, can be converted into checking some constructed matrix. Meanwhile, two algorithms are developed to verify the detectability based on a novel algebraic framework. Lastly, one prototypical numeric example is provided to validate the effectiveness of our theoretical approach. Note that the current results will help us to further investigate the detectability-based enforcement of networked systems.

Keyword : Communication delays, networked initial-state detectability, networked systems, semi-tensor product.

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