Robust Design Specifications

A control system is robust if it remains stable and achieves certain performance criteria in the presence of possible uncertainties as discussed in Chap. 2. The robust design entails to find a controller, for a given system, such that the closed-loop system is robust. The \(\mathcal{H}_{\infty}\) optimization approach and its related approaches, being developed in the last two decades and still forming an active research area, have been shown to be effective and efficient robust design methods for linear, time-invariant control systems. We will first introduce in this chapter the Small-Gain Theorem, which plays an important role in the \(\mathcal{H}_{\infty}\) optimization methods, and then discuss the stabilization and performance requirements in robust designs using the \(\mathcal{H}_{\infty}\) optimization and related ideas. We introduce also the so-called structured singular value which is used in the robust analysis and design in case of structured uncertainties.

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