On robust admissibility condition for descriptor systems with convex polytopic uncertainty

In this paper, we first establish an LMI condition for descriptor systems under which the system is regular and impulse-free, and all finite poles are located in a class of LMI regions. Then, for descriptor systems with convex polytopic uncertainty, we obtain a sufficient LMI condition to test robust admissibility of the considered system. The results of this paper extend the existed results of normal systems to descriptor systems. The robust admissibility condition of the continuous-time can be obtained as special case. Finally, a numerical example is given to illustrate the results.