Weighted H ^∞ mixed-sensitivity minimization for distributed parameter plants under sampled-data control

This paper considers the problem of designing near-optimal finite-dimensional sampled-data controllers for single-input single-output (SISO) and possibly unstable distributed parameter plants. A weighted H ^∞-style mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a `natural' finite-dimensional sampled-data optimization. Conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. This technique also assumes and exploits the fact that the plant coprime factors 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 proofs and construction given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straight forward control design approach for a large class of SISO and possibly unstable distributed parameter systems under sampled-data control.