Sampled-Data Piecewise Affine Differential Inclusions

This paper addresses exponential stability and stabilization of sampled-data piecewise affine differential inclusions (PWADI) with an unknown nonuniform sampling rate. The contributions of this paper are threefold. First, given a controller, sufficient conditions for exponential stability of closed-loop sampled-data PWADI are presented using a piecewise smooth Krasovskii functional. Second, assuming the controller is piecewise linear and the Krasovskii functional is piecewise quadratic, the stability conditions are cast as linear matrix inequalities (LMIs). Third, sufficient conditions for sampled-data controller synthesis for PWADI are formulated in terms of LMIs, with the maximum allowable sampling period as a parameter. The effectiveness of the approach is shown via a PWADI example that is motivated by a nonlinear system.