Weighted H∞ mixed-sensitivity minimization for stable MIMO distributed-parameter plants

This paper considers the problem of designing near-optimal finite-dimensional compensators for stable multiple-input multiple-output (MIMO) distributed-parameter plants. A weighted H∞ mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a 'natural' finite-dimensional optimization. Apriori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the distributed-parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. Although the proofs assume and exploit the fact that the plant can be approximated uniformly by finite-dimensional systems, it is indicated how compact approximants could be used. 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 constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straightforward control design approach for a large class of MIMO distributed-parameter systems.