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 sampled-data 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 jump-flow 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 continuous-time 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.