Stability Analysis And Stabilization Decomposition For The Large-Scale Systems With Time-Delay

The stability analysis and stabilization decomposition problems were put forward for the large-scale systems with time-delay by using the decomposition method.In the first part,the stability analysis problem was put forward for the time-invariant large-scale systems with time-delay including retarded type and neutral type by using the partial decomposition method. With the stability of the isolated subsystems without time-delay some sufficient criterions for the asymptotical stability of the whole system were obtained by making the Lyapunov functional and Lyapunov function with Razumikhin condition. Those sufficient criterions including delay-dependent criterion and delay-independent criterion extended the range of unidirectional interconnected items to some extent although its could not be selected with random due to the time-delay. Compared with the equivalence method of Lyapunov decomposition, an example show that the conclusions in this paper were better than the former ones and can be optimized by selecting parameters. Furthermore, the conclusion of this paper is easy to verify.In the second part of this paper, the stabilizing decomposition problem was put forward for the large-scale control system with time-delay including retarded type and neutral type by making the Lyapunov functional and Lyapunov function with Razumikhin condition and using the Schur theorem. Compared with the former conclusion,the sufficient criterions in this paper including delay-dependent criterion and delay-independent criterion were simpler,less conservative and easier to verify. In the end of this part,the equivalence method of Lyapunov decomposition was used to study the neutral type time-varying large-scale control system because the method of this paper is invalid.