ASYMPTOTIC STABILITY OF NONLINEAR DELAY-DIFFERENCE SYSTEM VIA MATRIX INEQUALITIES AND APPLICATION

Abstract

In this paper, we derive a sufficient condition for asymptotic stability of the zero solution of delay-difference system of nonlinear delay-difference system in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method. The result is applied to obtain new stability condition in terms of certain matrix inequalities for some class of nonlinear delay-difference system such as delay-difference system of nonlinear delay-difference system with multiple delays in terms of certain matrix inequalities. Our results can be well suited for computational purposes.