Stability Analysis of Time-Delay Systems by Nonlinear Approximation

We consider a nonlinear complex (large-scale) system with time delay. It is assumed that the corresponding isolated subsystems are homogeneous, and the zero solutions of the sub- systems are asymptotically stable when delay is equal to zero. By the Lyapunov direct method, and the Razumikhin approach, delay-independent stability conditions for the complex system are obtained. These conditions are formulated in terms of solvability of auxiliary systems of al- gebraic inequalities. An example is given to demonstrate effectiveness of the presented results.