A convex approach to stabilization of sampled-data piecewise affine slab systems

This paper addresses exponential stability and stabilization of piecewise affine (PWA) slab systems with piecewise linear (PWL) sampled-data feedback. The PWL controller is assumed to be located in the feedback loop between a sampler with an unknown nonuniform sampling rate and a zero-order-hold. Convex Krasovskii-based sufficient conditions are proposed for exponential stability and stabilization of the sampled-data PWA slab system. The main contributions of this paper are twofold. First, the direct sampled-data controller synthesis problem for PWA slab systems is formulated as a convex optimization program with the maximum allowable sampling period as a parameter. Second, sufficient conditions for exponential stability of PWA sampled-data systems are presented. The stability analysis and controller synthesis conditions are cast as linear matrix inequalities. The results are successfully applied to a unicycle path following problem.