Generalized Lyapunov and invariant set theorems for nonlinear dynamical systems

✍ Scribed by VijaySekhar Chellaboina; Alexander Leonessa; Wassim M. Haddad

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 103 KB
• Volume: 38
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(99)00076-6

✦ Synopsis

In this paper we develop generalized Lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the Lyapunov function and the system dynamics are removed. In particular, local and global stability theorems are given using lower semicontinuous Lyapunov functions. Furthermore, generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over ÿnite intervals of the closure of generalized Lyapunov level surfaces. The proposed results provide transparent generalizations to standard Lyapunov and invariant set theorems.