A MIXED L-INFINITY/H-INFINITY OPTIMIZATION APPROACH TO ROBUST CONTROLLER-DESIGN

In spite of its practical importance, the problem of designing controllers capable of satisfying mixed time/frequency domain performance requirements under model uncertainty remains, to a large extent, open. In this paper we propose a design procedure for minimizing the maximum amplitude of a regulated error to a specified input while, at the same time, addressing model uncertainty through bounds on the H-infinity norm of a relevant transfer function. This problem is of interest in optimal tracking applications where the objective is to achieve minimum tracking error while, at the same time, maintaining an adequate robustness level. We show that for the SISO case, the problem can be solved by solving sequence of problems, each one consisting of a finite-dimensional convex optimization and an unconstrained Nehari approximation problem.