Abstract We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, terms small-gain conditions. Such conditions have played an important role the finite-dimensional theory, but are relatively unexplored infinite-dimensional setting, yet. Our results applicable to spaces that a normal and generating cone. Moreover, we show our cri...

ABSTRACT. This paper studies impulsive discrete systems with time delay. Several criteria on uniform stability and uniform asymptotic stability are established by utilizing the Razumikhin technique. Both linear and nonlinear impulsive discrete systems with time delay are investigated. These stability criteria show that impulses can be used to stabilize a unstable system. Some numerical examples...