Robust stability and stabilization of uncertain delay systems

This paper considers the problem of robust stability and stabilization of uncertain time delay systems. We focus on the class of Metzlerian delay systems and use the interesting properties of Metzler matrix to provide the necessary ingredients for the main results of the paper. It is shown that Metzlerian delay system is asymptotically stable if and only if the Metzlerian system without delay* is asymptotically stable. This fact allows one to establish strong results on constrained stabilization for delay systems. The robust stability of Metzlerian delay system is also revisited and, without requiring long derivation, direct formulas for calculating the stability radius of this class of systems are provided. Finally, we consider the problem of constrained robust stabilization of interval delay systems and outline an LMI based solution for it. The paper concludes with two numerical examples to support the theoretical results.