Stabilization of a class of state-constrained nonlinear switched systems in lower triangular form

Abstract

In this paper, we deal with the stabilization problem for a class of switched nonlinear systems in lower triangular form subject to constraints on the state. To prevent state from transgressing the constraints, we employ the ideal p-times differentiable unbounded functions, which grow to infinity when their arguments approach domain boundaries. Based on the backstepping technique, we propose a constructive method to design controllers for the switched system. Furthermore, we show that asymptotic stabilization is achieved without violation of the constraints and all closed-loop signals remain bounded, when a mild requirement on the initial values is imposed. Finally, the effectiveness of the proposed results is demonstrated using a simulation example.