Stabilization of sampled-data Lur´e systems with nonuniform sampling

The paper addresses the problem of Lur´e sampled-data control design with non uniform sampling. It is shown that this problem can be treated using a methodology based on Euler approximate discrete time models associated to a formulation of the problem in the switched systems framework. Given a finite set of sampling periods, the problem is formulated as a stabilization problem for discrete-time switched Lur´e systems with norm bounded uncertainty. A quadratic criterion is used to take into account possible penalties on the sampling periods. Sufficient conditions are provided to compute both the controller gains and the active sampling period. The approach takes into account the inter-sample behaviour and provides stability guarantees for the exact Lur´e sampled-data system.