Decentralized stabilization of large-scale linear continuous systems with N x N time-varying delays

In this paper, a decentralized stabilization condition for large-scale linear continuous systems with N x N time-varying delays is established under a decomposition case of the interconnections. Based on a new stability theor ern for a general type of retarded dynamic systems, the results are derived by using the Lyapunov function instead of the Lyapunov functional. During the derivation, a new technique for estimating the derivative of the Lyapunov function for the solution of the system under consideration is used so that the case of N x N time-varying delays can be dealt with as least conservatively as possible. It is noted that the stabilization condition obtained by using the proposed technique is better than those obtained by using the existing Razumikhin-type techniques in the literature. An example with three interconnected subsystems is given to illustrate the proposed method and to show the design of the local memoryless state feedback controllers.