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(alpha, r) in the presence of parametric uncertainties. An example is finally provided for illustrating our main results. Copyright (C) Published by Elsevier Science Ltd