Stability analysis of a type of nonlinear time-delay control systems

The time delay of Lurie nonlinear systems, in which the origin of the nonlinear systems is the absolute stability, is estimated by using a Liapunov-Razumikhn function. Two sufficient conditions are obtained about absolutely stable criteria of nonlinear systems. A numerical example illustrates the effectiveness of the presented algorithm. We find that the key problem is how to choose tau. The value of tau depends on the set D that relates to Liapunov matrix Q. So the optimization (Q(best)-tau(max)) is our objective. By using computer aided tools and Liapunov matrix equations, we can obtain the optimization r.