Stabilization and performance synthesis for systems with repeated scalar nonlinearities

Author

Chu, Yun-Chung ; Glover, Keith

Author_Institution

Dept. of Eng., Cambridge Univ., UK

Volume

44

Issue

3

fYear

1999

fDate

3/1/1999 12:00:00 AM

Firstpage

484

Lastpage

496

Abstract

The class of nonlinear systems described by a discrete-time state-equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered. Given a plant of this form, sufficient conditions are derived for: 1) the parametrization of all controllers of the same form such that the closed loop is stable in the sense of a diagonally dominant Lyapunov function; and (2) the synthesis of a controller of the same form so that the induced norm of the closed loop is under a prescribed level. Several of these conditions can be written into linear matrix inequalities

Keywords

Lyapunov methods; control system synthesis; discrete time systems; matrix algebra; nonlinear systems; recurrent neural nets; stability; transforms; Lyapunov function; closed loop systems; diagonal stability; discrete-time systems; gain scheduling; linear fractional transforms; linear matrix inequality; nonlinear systems; recurrent neural networks; repeated scalar nonlinearity; sufficient conditions; Linear matrix inequalities; Lyapunov method; Network synthesis; Neural networks; Nonlinear equations; Nonlinear systems; Recurrent neural networks; Stability; Sufficient conditions; Symmetric matrices;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.751343

Filename

751343