Title :
Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities
Author :
Chu, Yun-Chung ; Glover, Keith
Author_Institution :
Dept. of Eng., Cambridge Univ., UK
fDate :
3/1/1999 12:00:00 AM
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. Sufficient conditions are derived for the stability and induced norm of such systems using positive definite diagonally dominant Lyapunov functions or storage functions, satisfying appropriate linear matrix inequalities. Results are also presented for model reduction errors for such systems
Keywords :
Lyapunov methods; discrete time systems; matrix algebra; nonlinear systems; recurrent neural nets; reduced order systems; stability; Lyapunov functions; diagonal stability; discrete-time systems; induced norm; linear matrix inequality; model reduction errors; nonlinear systems; recurrent neural networks; repeated scalar nonlinearities; sufficient conditions; Artificial neural networks; Linear matrix inequalities; Linear systems; Nonlinear equations; Nonlinear systems; Observability; Recurrent neural networks; Reduced order systems; Stability; Sufficient conditions;
Journal_Title :
Automatic Control, IEEE Transactions on
