Necessary and Sufficient Stability Criterion and Stabilization for Positive 2‐D Continuous‐Time Systems with Multiple Delays. Issue 3 (7th May 2018)

• Record Type: Journal Article
• Authors: Duan, Zhaoxia; Ghous, Imran; Wang, Bing; Shen, Jian
• Is Part Of: Asian journal of control. Volume 21:Issue 3(2019)
• Page Start: 1355
• Page End: 1366
• Publication Date: 2018-05-07
• Subjects: Positive 2‐D systems -- 2‐D continuous‐time systems -- stability -- multiple delays -- stabilization -- delays; Automatic control -- Periodicals; Control theory -- Periodicals; 629.805
• DOI: 10.1002/asjc.1811
• Languages: English
• ISSNs: 1561-8625

Abstract

Abstract: 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.