Robust Stability of Switched-Interval Positive Linear Systems with All Modes Unstable Using the Φ-Dependent Dwell Time Technique

Abstract

In this study, some stability and robust stability conditions for switched positive linear systems in which all subsystems are unstable in continuous time and discrete time were obtained using the Φ-dependent dwell time technique and the discretized co-positive Lyapunov functions approach, respectively. The co-positive Lyapunov functions constructed in this study are functions of time during the dwell time, and after that, they are independent of time. In addition, the above method was applied to switched-interval positive systems, and corresponding conclusions are presented. The Φ-dependent dwell time technique used in this paper is more effective than the dwell time and mode-dependent dwell time used in other studies. The results are verified with an illustrative example.

Keywords

• Φ-dependent dwell time
• discretized co-positive Lyapunov functions
• robust stability
• unstable subsystems