ROBUST STABILITY OF NONLINEAR TIME-DELAY SYSTEMS WITH APPLICATIONS TONEURAL NETWORKS

In the first part of this paper we consider a family of nonlinear time -delay systems with uncertainties. For such systems, we present two ty pes of sufficient conditions for robust stability, One type involves d elay independent results while the other type involves delay dependent results, In the second part, we apply these sufficient conditions to a class of time-delay artificial neural networks and obtain practical criteria to test asymptotic stability of the equilibria of these time- delay artificial neural networks, with or without perturbations, These criteria require verification of the definiteness of a certain matrix , or verification of a certain inequality. Our results provide also a method of estimating the domain of attraction of the asymptotically st able equilibria of the time-delay neural networks, The applicability o f our results is demonstrated by means of three specific examples.