Abstract

Contraction property of dynamical systems, especially difference systems, is one of the qualitative properties which have attracted much attention from many researchers for recent decades. Contraction of dynamical systems has many practical applications which means that two trajectories of the system convergence to each other when the time reaches to positive infinity. In this paper, by improving some existing approaches, we present a new approach to contraction problem of a class of nonlinear time-varying delay difference system with continuous time. We generalize the definition of contraction to -contraction. Then, we give some new explicit sufficient criteria for -contraction and global exponential stability of the mentioned system. Furthermore, we investigate-contraction of perturbed difference systems with continuous time under nonlinear perturbations in which perturbations are general time-varying functions. Then we obtain a new explicit-contraction bound for such systems subject to nonlinear time-varying perturbations. The obtained theorems generalize some existing results in the literature as particular cases. An example is given to illustrate the obtained results.