Immersion and invariance stabilization for a class of nonlinear switched systems with average dwell time

Abstract An immersion and invariance (I&I) stabilization theorem for nonlinear switched systems with average dwell time is set up which provides a tool for analyzing the behavior of switched systems. Also, a method integrating the I&I technique and viability method is proposed to stabilize nonlinear switched systems with state constraints. Based on the proposed theorem, this paper further investigates the problem of I&I stabilization of nonlinear switched systems in feedback form and with state constraints represented by inequalities, when all target subsystems are stable as well as only some target subsystems are stable and others are not. State-feedback controllers for subsystems are obtained constructively and a class of switching signals with average dwell time is derived simultaneously. Finally, an application to a numerical example is given to illustrate the effectiveness of the proposed method.