Weighted H-infinity mixed-sensitivity minimization for stable distributed parameter plants under sampled-data control

This paper considers the problem of designing near-optimal finite-dimension al controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under sampled-data control. A weighted H-infinity-style m ixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a "natural" fini te-dimensional sampled-data optimization. A priori computable conditions ar e given on the approximants such that the resulting finite-dimensional cont rollers stabilize the sampled-data controlled distributed parameter plant a nd are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. This technique also assumes a nd exploits the fact that the plant can be approximated uniformly by finite -dimensional systems. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite- dimensional problem using a suitable finite-dimensional approximant. The co nstructions given are simple. Finally, it should be noted that no infinite- dimensional spectral factorizations are required. In short, the paper provi des a straight forward control design approach for a large class of MIMO di stributed parameter systems under sampled-data control.