Generalized Lyapunov and invariant set theorems for nonlinear dynamical systems

Author

Chellaboina, VijaySekhar ; Leonessa, Alexander ; Haddad, Wassim M.

Author_Institution

Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA

Volume

5

fYear

1999

fDate

1999

Firstpage

3028

Abstract

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 finite intervals of the closure of generalized Lyapunov level surfaces. The proposed results provide transparent generalizations to standard Lyapunov and invariant set theorems

Keywords

Lyapunov methods; nonlinear dynamical systems; set theory; stability; generalized Lyapunov theorem; generalized invariant set theorem; global stability theorem; local stability theorem; lower semicontinuous Lyapunov functions; nonlinear dynamical systems; Adaptive control; Aerodynamics; Aerospace engineering; Asymptotic stability; Control systems; Lyapunov method; Nonlinear dynamical systems; Nonlinear systems; Stability analysis; Switches;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 1999. Proceedings of the 1999

Conference_Location

San Diego, CA

ISSN

0743-1619

Print_ISBN

0-7803-4990-3

Type

conf

DOI

10.1109/ACC.1999.782317

Filename

782317