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"~ 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"~ 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.

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