Exponential stability and estimates for monotone and differential-difference systems

We present necessary and sufficient conditions for the exponential stability in the nonnegative cone and refine exponential estimates for solutions of systems of autonomous difference equations with monotone nondecreasing right-hand sides, including discontinuous ones, as well as for solutions of some class of systems of differential-difference equations with monotonicity. Unlike well-known criteria, the new ones are free of some additional assumptions on the right-hand sides of the considered models other than the original monotonicity conditions. We show that, in the nonsmooth and discontinuous cases, the traditional exponential stability conditions based on ??linearization?? can lead to negative or very coarse results.