ABSTRACT
We recall that the previous two chapters have a common denominator. Chapter 2 was concerned with the internal stability of open-loop systems and Chapter 3 dealt with closed-loop system stability under state-feedback. Therefore Chapter 3 was a natural extension of Chapter 2. We also adopted, in Chapter 3, H∞-bound as one tangible design criterion in synthesizing a feedback controller and considered uncertain systems with state and input delay. In this chapter, we expand this philosophy further and examine the robust H∞-control for different classes of uncertain time-delay systems. The results presented hereafter complement those of Chapter 3, but also add re sults on nonlinear, discrete-time as well as multiple-delay systems. It should be emphasized that in systems theory H∞ attenuation has been proven to be a very useful performance measure. Loosely speaking, if w(t) ∈ £2[0, ∞) is the exogenous input and z(t) is the controlled output then the γ-disturbance attenuation problem is to choose a state-feedback law u(t) = Ksx(t) which guarantees the closed-loop internal stability and ensures that
