Piecewise polynomial Lyapunov functions for a class of switched nonlinear systems

Abstract

This paper proposes sufficient conditions to the regional stability analysis of switched nonlinear systems with time-varying parameters. The nonlinear sub-modes of operation are described by means of differential-algebraic equations involving the state and an auxiliary nonlinear vector. We then use piecewise polynomial Lyapunov functions and a relaxation technique that lead to a convex characterization of the problem in terms of linear matrix inequalities.