Synthesis of digital optimal reduced-order compensators for asynchronously sampled systems

The synthesis of finite-horizon digital optimal reduced-order compensators is presented, for asynchronous and aperiodically sampled continuous-time systems. The dimensions of the compensator state are a priori fixed and may be time varying. Asynchronous and aperiodic sampling refers to a deterministic sampling scheme where an arbitrary, but a priori known, number of control variables is updated, and/or an arbitrary, but a priori known, number of outputs is sampled, at arbitrary, but a priori known, time instants. This sampling scheme generalizes most deterministic sampling schemes considered in the control literature. Through the use of an integral criterion the intersample behaviour is explicitly considered in the design. As a result, frequent, synchronous and periodic sampling is no longer necessary, which can be highly relevant in practice. Also the synthesis enables comparison of the optimal performance of reduced-order compensators as a function of their dimensions and the sampling scheme. The synthesis is illustrated with a numerical example