Optimal input matching in sampled data control systems

An optimal hybrid input matching (OHIM) controller is proposed to control linear time-invariant systems. The method is based on redesign of a desired pure continuous-time closed-loop system, and the controller is optimal in the sense that the L₂(0,∞)-norm of the discrepancy between the obtained sampled data and continuous-time output signals is minimized. The derivation of the controller consists of the following two elementary steps; (i) sampling and spectral factorization of a rational function that only depends on the open-loop system and (ii) solving a linear matrix equation, which depends on the external signals. The method is applicable to any continuous-time linear control system and to arbitrary deterministic external signals