Weighted H∞ optimization for stable infinite dimensional systems using finite dimensional techniques

An approximate/design approach is taken to the problem of designing near-optimal finite-dimensional compensators for scalar infinite dimensional plants. The criteria used to determine optimality are standard H^∞ weighted sensitivity and mixed-sensitivity measures. More specifically, it is shown that, given a `suitable´ finite-dimensional approximant for an infinite-dimensional plant, one can solve a `natural´ finite-dimensional problem to obtain a near-optimal finite-dimensional compensator. Moreover, very weak conditions are presented to indicate what a `suitable´ approximant is. In addition, it is shown that the optimal performance can be computed by solving a sequence of finite-dimensional eigenvalue/eigenvector problems rather than the typical infinite-dimensional eigenvalue/eigenfunction problem which appears in the literature