H∞ optimization for stable multivariable infinite-dimensional systems

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. A priori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the infinite-dimensional plant and are near-optimal. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a finite-dimensional problem using a suitable finite-dimensional approximant. A result on “actual” transfer function matrix convergence is also presented