On the stability of a family of nonlinear time-varying systems

Author

Wang, Kaining ; Michel, Anthony N.

Author_Institution

Dept. of Electr. Eng., Notre Dame Univ., IN, USA

Volume

43

Issue

7

fYear

1996

fDate

7/1/1996 12:00:00 AM

Firstpage

517

Lastpage

531

Abstract

In the present paper we investigate several types of Lyapunov stability of an equilibrium x_e of a family of finite dimensional dynamical systems determined by ordinary differential (difference) equations. By utilizing the extreme systems of the family of systems, we establish sufficient conditions, as well as necessary conditions (converse theorems) for several robust stability types. Our results enable us to realize a significant reduction in the computational complexity of the algorithm of Brayton and Tong (1979) in the construction of computer generated Lyapunov functions. Furthermore, we demonstrate the applicability of the present results by analyzing robust stability properties of equilibria for Hopfield neural networks and by analyzing the Hurwitz and Schur stability of interval matrices

Keywords

Hopfield neural nets; Lyapunov methods; computational complexity; difference equations; matrix algebra; nonlinear dynamical systems; robust control; stability; time-varying systems; Hopfield neural networks; Hurwitz stability; Lyapunov stability; Schur stability; computational complexity; computer generated Lyapunov functions; difference equations; finite dimensional dynamical systems; interval matrices; nonlinear time-varying systems; ordinary differential equations; robust stability properties; Computational complexity; Difference equations; Differential equations; Hopfield neural networks; Lyapunov method; Nonlinear equations; Robust stability; Stability analysis; Sufficient conditions; Time varying systems;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.508171

Filename

508171