Finite -induced gain and -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 L 2 -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 λ -contractivity as large as possible or for obtaining a L 2 -gain as small as possible. A numerical example illustrates the proposed approaches.