Sampled-data controller synthesis using dissipative linear periodic jump-flow systems with design applications

In this paper, we will propose linear-matrix-inequality-based techniques for the design of sampleddata controllers that render the closed-loop system dissipative with respect to quadratic supply functions, which includes passivity and an upper-bound on the system's H ∞ -norm as a special case.To arrive at these results, we model the sampled-data control system as a linear periodic jumpflow system, study dissipativity in terms of differential linear matrix inequalities (DLMIs) and then convert these DLMIs into a single linear matrix inequality.We will present three applications of these synthesis techniques: (1) passivity-based controller synthesis, as found in teleoperations, (2) input-output-response matching of a continuous-time filter with a discrete-time filter (by minimizing the H ∞ -norm of a generalized plant) and (3) a sampled-data controller redesign problem, where the objective is to find the best sampled-data controller, in the H ∞ -norm sense, for a given continuoustime controller.We will show that synthesizing sampled-data controllers leads to better closed-loop system behaviour than using a Tustin discretization of a continuous-time controller.