L2 -induced gain for discrete-time switched Lur'e systems via a suitable Lyapunov function

International audience; This paper deals with discrete-time switched Lur'e systems including an additional saturated input and a bounded energy disturbance. Two control design issues are investigated related to the L2-induced gain and the rejection of disturbance. An common optimization problem under LMI conditions and differing from the cost function to optimize, is provided to offer a solution to the both problems. The main approach is to upper bound a criterion with a suitable Lur'e type Lyapunov function. Numerical examples are given to underline the efficiency of our approach and to allow a discussion with the literature.