Optimal D-stable control for discrete multiple time-delay systems with parametric uncertainties

The robustly optimal D-stable problem is considered in this study for discrete multiple time-delay systems with parametric uncertainties. A discrete uncertain multiple time-delay system can be transformed into another system with no delay by properly defining new state variables. The problem of optimization of discrete-time systems with multiple time delays is consequently reduced to a standard discrete linear quadratic regulator problem A robust criterion of D-stability is derived on the basis of D-pole placement technique to show that the optimal control law not only minimizes the discrete linear quadratic performance index but also simultaneously guarantees that all poles of the closed-loop system remain inside the specified disk D(α,r) in the presence of parametric uncertainties. An example is finally provided for illustrating our main results.