Finite L2L2-induced gain and λλ-contractivity of discrete-time switching systems including modal nonlinearities and actuator saturations

The paper addresses two control problems of discrete-time switching systems subject to modal nonlinearities satisfying sector conditions, actuator saturations and additive L2L2-bounded disturbances. Such switching systems consist of a finite family of discrete-time processes that are supervised by logical decision-making algorithms. Conditions based on LMIs are provided for synthesizing the control gains and for obtaining regions of absolute λλ-contractivity as large as possible or for obtaining a L2L2-gain as small as possible. A numerical example illustrates the proposed approaches.