A finite polynomial algorithm for computing the largest eigenvalue of the "Toeplitz+Hankel" operator of the H∞ problem

We construct a finite algorithm for computing the achievable feedback performance evaluated in the H^∞ sense. This finite algorithm, which contrasts with previous iterative procedures, reduces the problem of evaluating the achievable performance to the computation of the zeros of a polynomial matrix. It is based on a strange connection between the H^∞ and linear-quadratic problems--a "Toeplitz + Hankel" operator shared by both problems.