Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities

Authors
Citation
Yc. Chu et K. Glover, Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities, IEEE AUTO C, 44(3), 1999, pp. 471-483
Citations number
26
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN journal
00189286 → ACNP
Volume
44
Issue
3
Year of publication
1999
Pages
471 - 483
Database
ISI
SICI code
0018-9286(199903)44:3<471:BOTINA>2.0.ZU;2-E
Abstract
The class of nonlinear systems described by a discrete-time state equation containing a repeated scalar nonlinearity as in recurrent neural networks i s considered. Sufficient conditions are derived for the stability and induc ed norm of such systems using positive definite diagonally dominant Lyapuno v functions or storage functions, satisfying appropriate linear matrix ineq ualities. Results are also presented for model reduction errors for such sy stems.