D-stability for a class of discrete descriptor systems with multiple time delays

In this paper, the research on discrete descriptor systems is extended to include discrete multiple time-delay descriptor systems. The impulse-free and D-stability problem for a class of discrete descriptor systems with multiple time delays is investigated. A delay-dependent criterion is first derived to guarantee that the system is proper. A delay-dependent stability criterion in terms of spectral radius is then presented to ensure the D-stability of the system. Furthermore, a delay-dependent criterion is proposed to guarantee that the system is nebular, impulse-free, and D-stable. Finally, a numerical example is provided to illustrate our main results.