Stability criteria for positive linear discrete-time systems

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 criteria can be considerably simplified if cone has non-empty interior or operator under consideration is quasi-compact. To place into context include overview known (and not necessarily positive) operators provide full proofs several folklore characterizations from this domain.