A Polynomial Solution to an H∞ Robust Stabilization Problem

In this paper, we present a polynomial solution to a particular H-infinity control problem, which arises in the robust stabilization of a SISO plant when the uncertainty is described by the gap metric, v-gap metric, pointwise gap metric, or normalized corprime factor perturbation. Compared with the existing state space solution, the polynomial solution appears simpler and more elementary. It boils down to a rational function pole-placement problem and hence is equivalent to a polynomial Diophantine equation. The derivation of this polynomial solution is based on the existing results of the Nehari problem. We first reduce the original problem to the Nehari problem, and then find the closed-loop characteristic polynomial from the solution to the Nehari problem. Finally, we obtain the desired controller by rational function pole-placement.