A polynomial solution to the scalar 4-block H ∞ general distance problem

Abstract

The H ∞ mixed sensitivity with measurement noise problem is considered for the scalar case using a polynomial description. The problem results in a 4-block general distance scalar problem which is solved in a general way by using a polynomial equation approach. As an example, the solution is then applied to the mixed sensitivity with measurement noise problem where all relevant simplifications are carried out. The solution requires solving two spectral factorization problems and one linear polynomial equation. Further, new insight into the connections with the Nehari problem is provided.