Mixed discrete/continuous specifications in sampled-data H2-optimal control

The increasing use of digital equipment in control in the last half century made a tremendous impact on controller design methodology. On the other hand, it had little effect on the control problem formulation: the control goals to a large extent still remain those of the analog world. The goal of this paper is to introduce and justify a new approach to sampled-data control system design, which enables one to account for the special opportunities, introduced by the employment of digital equipment. The essence of this approach is the simultaneous treatment of both continuous- and discrete-time performance requirements; hence, mixed discrete/continuous specifications (MDCS). In the paper, the sampled-data H2 MDCS problem is formulated and solved. As a by-product of the MDCS treatment several novel technical results are obtained. Illustrative examples, demonstrating the potential benefits of the proposed approach are presented.