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Necessary and Sufficient Stability Criterion and Stabilization for Positive 2‐D Continuous‐Time Systems with Multiple Delays
Author(s) -
Duan Zhaoxia,
Ghous Imran,
Wang Bing,
Shen Jian
Publication year - 2019
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1811
Subject(s) - control theory (sociology) , stability (learning theory) , mathematics , exponential stability , simple (philosophy) , state (computer science) , linear system , stability conditions , control (management) , computer science , nonlinear system , discrete time and continuous time , mathematical analysis , algorithm , philosophy , statistics , physics , epistemology , quantum mechanics , machine learning , artificial intelligence
This paper addresses the stability and control problem of the linear positive two‐dimensional (2‐D) continuous‐time systems in Roesser model with multiple time delays. The contribution lies in two aspects. First, a simple novel proof is provided to establish necessary and sufficient conditions of asymptotic stability for 2‐D continuous delayed systems. It turns out that the magnitude of delays has no any impact on the stability of these systems, which is completely determined by the system matrices. Second, a necessary and sufficient condition for the existence of state‐feedback controllers is proposed for general delayed 2‐D systems, which ensures the non‐negativity and the stability of the resulting closed‐loop systems. Two examples are given to validate the proposed methods.