Lyapunov functions for time varying systems satisfying generalized conditions of Matrosov theorem

Abstract

The classical Matrosov theorem concludes uniform asymptotic stability of time varying systems via a weak Lyapunov function (positive definite, decrescent, with negative semi-definite derivative along solutions) and another auxiliary function with derivative that is strictly non-zero where the derivative of the Lyapunov function is zero [10]. Recently, several generalizations of the classical Matrosov theorem that use a finite number of Lyapunov-like functions have been reported in [5]. None of these results provides a construction of a strong Lyapunov function (positive definite, decrescent, with negative definite derivative along solutions) that is a very useful analysis and controller desi..