Zhi Liu, Xian-Fu Zhang*, and Yu-Zhen Wang
International Journal of Control, Automation, and Systems, vol. 15, no. 6, pp.2628-2635, 2017

Abstract : "This article investigates the robustness of switched multiple equilibrium points systems (SMEPSs) with unstable subsystems. Each subsystem has a unique equilibrium point that is different from all equilibrium points of the other subsystems. Unlike the most commonly used Lyapunov function method, the analytical solutions and numerical solutions are calculated to analyze the boundedness of the solutions for perturbation discrete-time and continuons-time SMEPSs, respectively. The given perturbation systems have good robustness if the ratio of total dwell time of unstable subsystems and the total dwell time of stable subsystems is less than or equal to a constant. A numerical example is employed to validate the correctness of the theoretical results."

Keyword : Multiple equilibrium points, robustness, switched system, unstable subsystem.