Robust Reset Controller Design for Switched Nonlinear Uncertain Systems

Abstract

This paper presents a design of a robust switching reset controller for a class of nonlinear uncertain switched systems. We consider the norm-bounded time-varying parameter uncertainties in switched nonlinear systems obeyed by the average dwell-time switching signal. The proposed switching reset controller uses the measured output in resetting the controller’s states, whereas the previous studies did not. A weighted mixed $\mathcal {L}_{2}/l_{2}$ -gain is introduced to take into account the discrete disturbances induced by the measured output when resetting the controller’s states. The proposed reset controller and switched nonlinear uncertain plant form a closed-loop system that is a class of nonlinear impulsive switched uncertain systems. Hence, we first provide sufficient conditions for the $\mathcal {L}_{2}$ stability of the nonlinear impulsive switched uncertain systems. Based on the conditions, we propose linear matrix inequality (LMI)-based design conditions to choose the dynamic output feedback control and output feedback reset laws guaranteeing the weighted mixed $\mathcal {L}_{2}/l_{2}$ -gain performance of the controlled systems with continuous and discrete disturbances. Numerical examples demonstrate the effectiveness of the proposed method.

Keywords

• Impulsive switched systems
• L₂-stability
• linear matrix inequality
• nonlinear uncertain systems
• reset control systems