HINF interpolation of rational matrices

Abstract

The problem of minimizing the L∞-norm of some stable rational matrix E(s) subject to two basic types of matrix interpolation constraints is considered: given antistable rational matrices ̄N(s) and ̄M(s), the interpolating matrix E(s) is required to satisfy either the condition ̄N(s)E(s) = ̄M(s) or the condition that ̄N(s)E(s) has an unstable projection equal to ̄M(s). These two kinds of constraints are directly related to model-matching problems arising from H∞ optimal control. Specific conditions on ̄N(s) and ̄M(s) for the interpolation problems to be well-posed are discussed and closed-form characterizations for both optimal and suboptimal solutions in E(s) are provided. The analysis is based on a state-space setting and the results are suitable for computational purposes.