Robust Stabilization for Uncertain Non-Minimum Phase Switched Nonlinear System under Arbitrary Switchings

Abstract

This paper addresses the problem of stabilization of non-minimum phase switched nonlinear systems where the internal dynamics with symmetries or non-symmetries of each mode may be unstable. The authors initially build a stabilizing Lyapunov controller for each mode in order to stabilize its own unstable internal dynamics. The proposed approach is based on the exact input-output feedback linearization technique and the Lyapunov stability theory. The stability results for non-minimum phase switched nonlinear systems with arbitrary switching rules are then obtained using generalized Gronwall–Bellman inequalities. Finally, numerical examples are provided to demonstrate the efficacy of the achieved results.

Keywords

• uncertain non-minimum phase systems
• exponential stability
• input–output feedback linearization
• generalized Gronwall–Bellman inequalities