Stability criteria for large-scale time-delay systems: the LMI approach and the Genetic Algorithms

This paper addresses the asymptotic stability analysis problem for a class of linear large-scale systems with time delay in the state of each subsystem as well in the interconnections. Based on the Lyapunov stability theory, a delay-dependent criterion for stability analysis of the systems is derived in terms of a linear matrix inequality (LMI). The results are improved by the application of the genetic algorithms. Finally, a numerical example is given to demonstrate the validity – flexibility and sharpness – of the proposed result.