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

The classical Matrosov theorem concludes uniform asymptotic stability of time varying systems via a weak Lyapunov function (positive definite, decrescent, with negative semidefinite derivative along solutions) and another auxiliary function with derivative that is strictly non-zero where the derivative of the Lyapunov function is zero [M1]. Recently, several generalizations of the classical Matrosov theorem have been reported in [LPPT]. None of these results provides a construction of a strong Lyapunov function (positive definite, decrescent, with negative definite derivative along solutions) which is a very useful analysis and controller design tool for nonlinear systems. Inspired by generalized Matrosov conditions in [LPPT], we provide a construction of a strong Lyapunov function via an appropriate weak Lyapunov function and a set of Lyapunov-like functions whose derivatives along solutions of the system satisfy inequalities that have a particular triangular structure. Our result...

• Type: Journal
• Year: 2007
• Where: MCSS
• Authors: Frédéric Mazenc, Dragan Nesic
• Keywords: Control Systems, Lyapunov Functions, MCSS 2007, Strong Lyapunov Function, Weak Lyapunov Function