Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities
- 1 March 1999
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 44 (3) , 471-483
- https://doi.org/10.1109/9.751342
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
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