Stability and Stabilization of Distributed time Delay Systems

This paper is dedicated to the stability and stabilization lization of state-distributed delay systems. The key idea is to express the distributed delay system as a bary centric sum of linear point wise time delay systems. By using this reformulation, new stability criterion is proposed and is formulated in the form of Linear Matrix Inequality. These conditions for the stability of the system are obtained by using a Lyapunov Krasovskii functional. Based on this stability criterion, new types of controllers, taking into account the delayed part, are designed to ensure the asymptotic stability of the system. Several examples illustrate the proposed method.