A sufficient condition for asymptotic stability of discrete-time interval system with delay.
We study non-autonomous rational difference equations. Under the assumption of a periodic non-autonomous parameter, we show that a well known trichotomy result in the autonomous case is preserved in a certain sense which is made precise in the body of the text. In addition we discuss some questions regarding whether periodicity preserves or destroys boundedness.
In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level ”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum...