Disturbance rejection of switched discrete-time systems with saturation nonlinearity

This paper addresses the problem of disturbance rejection for switched discrete-time linear systems subject to actuator saturations. An analysis condition is derived based on the switched saturation-dependent Lyapunov functions (SS-DLF) under which trajectories starting from a level set will remain inside an outer level set. An algorithm is developed to estimate the maximal norm of the exogenous disturbance that can be rejected by systems. Furthermore, upper bound of regional L₂-gain for exogenous disturbance is minimized. All the results are obtained by exploiting switched saturation-dependent Lyapunov functions (SSDLF) and presented in terms of linear matrix inequalities (LMIs). A numerical example is given to show the effectiveness of the proposed methods.