Stability and stabilisation for switched impulsive positive systems

Abstract

Abstract The current study is dedicated to addressing the stability and weighted L1‐gain performance analysis of switched impulsive positive systems (SIPSs). Firstly, by designing a novel multiple piecewise‐continuous copositive linear Lyapunov function and using the mode‐dependent average dwell time (MDADT) switching method, improved stability conditions that are able to achieve a tighter dwell time bound are developed. It is shown that the system under study is stable and possesses an attenuation property under the designed switching signals. Secondly, with the above stability conditions, a more effective controller design strategy has been proposed. The solved controllers are both quasi‐time dependent and mode‐dependent. Moreover, the constraint on the rank of the controller and the computation burden caused by iteration algorithm used in literature are relaxed. Finally, the feasibility and superiority of the proposed strategies are verified by some simulations.

Keywords

• Control system analysis and synthesis methods
• Stability in control theory
• Time-varying control systems
• Distributed parameter control systems
• Linear control systems