Robust D-stability and D-stabilization of descriptor discrete-time linear systems with polytopic uncertainties and multiple delays

This paper focuses on the problem of delay-dependent robust D-stabilization for a class of descriptor discrete-time linear systems with polytopic uncertainties and multiple state delays. New delay-dependent D-stability criteria are presented, and thereby, the problem of D-stabilization is solved. It is shown that the addressed problem can be solved if the corresponding developed linear matrix inequalities are feasible. The presented robust D-stabilizing state feedback control law guarantees the closed loop systems is robustly D-stable in spite of parameter uncertainties and state delays. Numerical examples are employed to show the usefulness of the proposed results.