Exact Detectability of Discrete-Time and Continuous-Time Linear Stochastic Systems: A Unified Approach

• 成果类型: Article
• 署名作者: Dragan, Vasile; Costa, Eduardo Fontoura; Popa, Ioan-Lucian; Aberkane, Samir
• 署名单位: Institute of Mathematics of the Romanian Academy; Romanian Academy; Academy of Romanian Scientists (AOSR); Universidade de Sao Paulo; 1 Decembrie 1918 University Alba Iulia; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Universite de Lorraine
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3134633
• 发表日期: 2022
• 页码: 5730-5745
• 关键词: stochastic systems; Markov processes; Time-varying systems; STANDARDS; Linear systems; switches; Symmetric matrices; Exact detectability; Popov-Belevich-Hautus (PBH) test; Stochastic systems

摘要

This article is devoted to the problem of detectability of a large class of linear stochastic systems with time varying coefficients simultaneously affected by state multiplicative white noise perturbations and Markovian switching. The main contribution of this article is to propose a Popov-Belevich-Hautus-type test, which is equivalent to the detectability of the considered stochastic systems in the sense that all unstable modes produce some nonzero output. The proposed setting unifies in some sense the discrete-time and continuous-time ones, dissimilarly to the vast majority of existing works that study discrete and continuous time separately.