Bounds of the induced norm and model reduction errors for a class of nonlinear systems

The class of nonlinear systems described by a discrete-time state equation containing a diagonal nonlinear term 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. Preliminary results are also presented for model reduction errors for such systems.