Automatica, Vol.36, No.10, 1443-1456, 2000
Performance with regulation constraints
We study the problem where we have a regulation (asymptotic tracking) requirement together with a performance requirement for continuous-time systems. Typically, we measure performance by the H-2 or H-infinity norm of a chosen transfer function matrix although any other norm such as the L-1 norm could be used. In the case when the performance is measured by the H-2 norm, there is no loss in performance due to the regulation constraint. On the other hand, when the performance is measured by the H-infinity norm, there exists in general certain loss of performance due to the regulation constraint, and we explicitly characterize such a loss. Determining suitable controllers for a given system with both regulation and performance constraints requires solving only an unconstrained optimization problem for an auxiliary system which is explicitly constructed here.