A new method for stability analysis of nonlinear discrete-time systems

Author

Barabanov, Nikita E. ; Prokhorov, Danil V.

Author_Institution

Dept. of Math., North Dakota State Univ., Fargo, ND, USA

Volume

48

Issue

12

fYear

2003

Firstpage

2250

Lastpage

2255

Abstract

We address the problem of global Lyapunov stability of discrete-time systems with known coefficients. We develop a method for reduction of dissipativity domain effectively testing if the system has a convex Lyapunov function. Our implementation is immediately applicable to differentiable systems with bounded nonlinearities, but the method proposed is more general and applicable to nondifferentiable systems with bounded right-hand sides. Our main application emphasis is on stability analysis of recurrent neural networks. We illustrate how to use our approach with examples.

Keywords

Lyapunov methods; asymptotic stability; control nonlinearities; discrete time systems; nonlinear systems; recurrent neural nets; Lyapunov stability; convex Lyapunov function; discrete-time system; dissipativity domain reduction; exponential stability; nondifferentiable system; nonlinear system; recurrent neural networks; sector monotone nonlinearity; stability analysis; Lyapunov method; Mathematics; Neural networks; Nonlinear dynamical systems; Nonlinear systems; Recurrent neural networks; Stability analysis; Stability criteria; System testing; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2003.820158

Filename

1254100