Backstepping design for global robust stabilisation of switched nonlinear systems in lower triangular form

Abstract

This article deals with the global robust stabilisation for a class of switched nonlinear systems under arbitrary switchings. The system under consideration is in lower triangular form and contains uncertainty. Both common Lyapunov function and state feedback controller are simultaneously constructed by backstepping such that the closed-loop system is globally robustly asymptotically stable under arbitrary switchings. Lastly, the design method proposed is extended to the uncertain switched nonlinear systems in nested lower triangular form to solve the global robust stabilisation problem under arbitrary switchings. Two examples are given to show the effectiveness of the proposed methods.