# 18: Performance of feedback systems


It is now time to turn to issues of performance. As noted in earlier chapters, performance specifications typically involve the closed-loop relations between the exogenous inputs $$w$$ and the regulated outputs $$z$$. These relationships are typically captured through the use of the signal and system norms. The analysis of a given controlled system usually involves evaluating the appropriate norms. The synthesis of a controller is a harder problem, as it involves picking a feedback compensator $$K$$ for which the closed-loop performance specifications are attained.

We begin our discussions with the single-input, single-output (SISO) case, and then move on to study multi-input, multi-output (MIMO) extensions. Much of what we present for the SISO case actually echoes what is done in "classical feedback control", although our perspective is somewhat more modern (or neo-classical or post-modern or ...!).

This page titled 18: Performance of feedback systems is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Mohammed Dahleh, Munther A. Dahleh, and George Verghese (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.