Switching control consistency of switched Lur´e systems with application to digital control design with non uniform sampling

In this paper, we study the consistency property in the case of discrete-time switched Lur´e systems. More precisely the min-switching strategy and quadratic upper bounds of the cost function are considered. We propose an optimization problem that provides the smallest upper bound of the cost function which satisfies the consistency in this nonlinear case. The difference with the linear case is illustrated using an academical example. Then the result is applied to design a sampled-data controller with non uniform sampling. A numerical example is proposed to highlight the features of the proposed strategy.