Steady‐state analysis of delay interconnected positive systems and its application to formation control. Issue 16 (8th September 2017)

• Record Type: Journal Article
• Authors: Ebihara, Yoshio; Peaucelle, Dimitri; Arzelier, Denis
• Is Part Of: IET control theory & applications. Volume 11:Issue 16(2017)
• Page Start: 2783
• Page End: 2792
• Publication Date: 2017-09-08
• Subjects: delay systems -- interconnected systems -- control system analysis -- control system synthesis -- multi‐agent systems -- frequency‐domain analysis -- matrix algebra -- multi‐robot systems; steady‐state analysis -- delay interconnected positive systems -- formation control -- nonnegative interconnection matrix -- positive subsystems -- multiagent systems -- positive dynamics -- constant communication delay -- steady‐state property -- frequency‐domain analysis; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2017.0315
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : This study is concerned with the analysis and synthesis of delay interconnected positive systems. For delay‐free cases, it has been shown very recently that the output of the interconnected positive system converges to a positive scalar multiple of a prescribed positive vector under mild conditions on positive subsystems and a non‐negative interconnection matrix. This result is effectively used for formation control of multi‐agent systems with positive dynamics. The goal of this study is to prove that this steady‐state property is essentially preserved under any constant (and hence bounded) communication delay. In the context of formation control, this preservation indicates that the desired formation is achieved robustly against communication delays, even though the resulting formation is scaled depending on initial conditions for the state. To ensure the achievement of the steady‐state property, the authors need to prove rigorously that the delay interconnected positive system has stable poles only except for a pole of degree one at the origin, even though it has infinitely many poles, in general. For the rigorous proof, we newly develop frequency‐domain ( s ‐domain) analysis for delay interconnected positive systems, which has not been studied for delay‐free cases.