Sum of Roots Characterization for Parametric State Feedback H_infty Control

This paper is concerned with the solution of state feedback H∞ control for a singleinput-single-output plant with parameters, and an algebraic approach that utilizes the so-called ‘sum of roots’ is developed. A method is firstly devised that computes a polynomial which contains the optimal cost as one of its roots. Furthermore it is shown that an optimal/suboptimal static feedback gain can be expressed in terms of plant parameters and the sum of roots. The proposed approach thus suggests that the sum of roots is useful for characterizing an achievable H∞ performance level as well as some H2 performance limitations.