Mixed L∞/H∞ controllers for SISO systems

This paper presents a rational mixed L_∞/H_∞ controller design method for SISO continuous time systems. The problem formulation involves minimizing the amplitude of a regulated output subject to a bounded fixed input of one closed-loop system while satisfying a frequency domain H_∞ norm constraint on another closed-loop system. We show that the optimal solution can be approximated arbitrarily closely, in terms of the time domain L_∞ norm, by solving a sequence of convex optimization over linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of this approach