Mixed L(infinity)/H-infinity controllers for SISO systems

This paper presents a rational mixed L(infinity)/H-infinity 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-infinity 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(infinity) norm, by solving a sequence of convex optimization over linear matrix inequalities. Numerical example is provided to demonstrate the effectiveness of this approach.