Positivity analysis for discrete-time descriptor systems with time delays

This paper is concerned with positivity analysis for discrete-time descriptor systems with time delays. At first, an explicit solution of such systems is given by using z-transform and inverse z-transform. Then, a set of necessary and sufficient conditions for positivity of discrete-time descriptor systems with time delays is presented under some conditions. In addition, based on the obtained conditions for positivity, systems with strictly positive state variables are concerned. Necessary and sufficient conditions to check strict positivity of state variables are obtained. Finally, an example is given to illustrate the effectiveness of the obtained results.