Stability Analysis of Time-Delay Systems by Nonlinear Approximation

Abstract: 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 subsystems 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 algebraic inequalities. An example is given to demonstrate effectiveness of the presented results