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 ...!).