Systems with Multiple and Distributed Delays

Abstract

In this chapter we will discuss the stability and robust stability of systems with multiple delays and distributed delays using time domain methods. We will not treat specific uncertainty type and only give results in the form of “matrix inequalities need to be satisfied for every point in the uncertainty set.” Of course, such a form cannot be directly implemented numerically. However, readers should not have difficulty applying the same principle discussed in Chapter 6 to reduce the problem to a finite number of matrix inequalities for some special type of uncertainties, such as subpolytopic uncertainty and norm-bounded uncertainty. Also, in view of the similarities between Razumikhin Theorem-based results and the ones based on simple Lyapunov-Krasovskii functional results, we will not discuss Razumikhin Theorem-based methods in this chapter.