H ^∞ sensitivity and mixed-sensitivity 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) infinite-dimensional plants. Two measures of optimality are used. First, we consider a weighted H ^∞ mixed-sensitivity measure which penalizes the control. Then we consider a standard weighted sensitivity measure. Controllers are generated by solving a 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 in the case of the mixed-sensitivity measure. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a finite-dimensional problem base on a suitable finite-dimensional approximant. For the sensitivity measure, convergence is proved but a priori conditions on the approximants are not presented in this note.