L₂-gain Analysis and Anti-windup Design of Discrete- time Switched Systems with Actuator Saturation

This paper investigates L2-gain analysis and anti-windup compensation gains design for a class of discrete-time switched systems with saturating actuators and L2 bounded disturbances by using the switched Lyapunov function approach. For a given set of anti-windup compensation gains, we firstly give a sufficient condition on tolerable disturbances under which the state trajectory starting from the origin will remain inside a bounded set for the corresponding closed-loop switched system subject to L2 bounded disturbances. Then, the upper bound on the restricted L2-gain is obtained over the set of tolerable disturbances. Furthermore, the anti-windup compensation gains aiming to determine the largest disturbance tolerance level and the smallest upper bound of the restricted L2-gain are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. A numerical example is given to illustrate the effectiveness of the proposed design method.