Generalized Lyapunov and invariant set theorems for nonlinear dynamical systems

In this paper we develop generalized Lyapunov and invariant set theorems fo r nonlinear dynamical systems wherein all regularity assumptions on the Lya punov function and the system dynamics are removed. In particular, local an d global stability theorems are given using lower semicontinuous Lyapunov f unctions. Furthermore, generalized invariant set theorems are derived where in system trajectories converge to a union of largest invariant sets contai ned in intersections over finite intervals of the closure of generalized Ly apunov level surfaces. The proposed results provide transparent generalizat ions to standard Lyapunov and invariant set theorems. (C) 1999 Elsevier Sci ence B.V. All rights reserved.