Stability of switched positive linear time-delay systems

• Published in: IET control theory & applications Vol. 13; no. 7; pp. 912 - 919
• Main Authors: Liu, Li-Juan, Zhao, Xudong, Wu, Di
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 30.04.2019
• Subjects: co‐positive Lyapunov–Krasovskii functional approach; delay systems; delays; linear programming; linear programming approach; linear systems; Lyapunov methods; mode‐dependent average dwell time; Special Issue: Theory of Positive Systems and Applications; stability; stability conditions; switched positive linear time‐delay systems; time‐varying systems; switched positive linear time-delay systems; time-varying systems; delay systems; mode-dependent average dwell time; delays; co-positive Lyapunov–Krasovskii functional approach; linear programming approach; linear programming; linear systems; stability conditions; stability; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2018.5170

In this study, the authors analyse the stability of switched positive linear time-delay systems. By developing a novel multiple discontinuous co-positive Lyapunov–Krasovskii functional approach, the stability conditions are established for switched positive time delay systems by a linear programming approach under mode-dependent average dwell time switching. Moreover, under average dwell time switching, the corresponding stability conditions are also proposed. It is shown that their results can obtain smaller lower bounds on dwell time. Finally, simulation results are given to show the effectiveness of their methods.