The Optimal H_∞ Norm of a Parametric System Achievable by an Output Feedback Controller

Abstract

H_∞ optimal control is one of the most successful achievements in the post modem control theory. In the H_∞ optimal control, we design a controller that minimizes the H_∞ norm of a given system. Although the algorithms to solve the problem have already been reported, they focus on numerical systems (systems without any unknown parameters) and, can not be applied for parametric systems (systems with unknown parameters). Given a parametric system, this paper presents an algorithm to compute the optimal H_∞ norm of the system achieved by an output feedback controller. The optimal H_∞ norm is expressed as 1/√φ(k), where φ(k), denotes a root of a bivariate polynomial. A numerical example is given to show the effectiveness of the algorithm.