A mixed H∞//H∞ optimization approach to robust controller design

Most realistic control problems involve both mixed time/frequency domain performance requirements and model uncertainty. However, the majority of controller design procedures currently available focus only on one aspect of the problem. 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_∞ 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 decoupled into a finite dimensional constrained optimization and an unconstrained Nehari approximation problem.