ABSTRACT
In designing feedback control systems, the stability of the resulting closed-loop system is a primary objective. Given a finite dimensional, linear time-invariant (FDLTI) model of the plant, G(s), the stability of the nominal closed-loop system based on this model, Figure 9.1, can be guaranteed through proper design: in the Nyquist plane for single-input, single-output (SISO) systems or by using well-known design methodologies such as LQG and H∞ for multi-input, multi-output (MIMO) systems. In any case, since themathematical model is FDLTI, this nominal stability can be analyzed by explicitly calculating the closed-loop poles of the system. It is clear, however, that nominal stability is never enough since themodel is never a true representation of the actual plant. That is, there are always modeling errors or uncertainty. As a result, the control engineer must ultimately ensure the stability of the actual closed-loop system, Figure 9.2. In other words, the designed controller, K(s), must be robust to the model uncertainty. In this article, we address this topic of stability robustness. We present a methodology to analyze the stability of the actual closed-loop system under nominal stability to a given model and a certain representation of the uncertainty.
