An efficient algorithm for finding the D-stability bound of discrete singularly perturbed systems with multiple time delays

In this paper, we present an original work on the D-stabilization problem of discrete singularly perturbed systems with multiple time delays. A new robust D-stability criterion in terms of stability radius is first derived to guarantee that all poles of the discrete multiple time-delay systems remain inside the specific disk D(alpha, r) in the presence of parametric uncertainties. Then, by using the technique of time-scale separation, we derive the corresponding slow and fast subsystems of a discrete multiple time-delay singularly perturbed system. The state feedback controls for the D-stabilization of the slow and the fast subsystems are separately designed and a composite state feedback control for the original system is subsequently synthesized from these state feedback controls. Thereafter, we derive a frequency domain epsilon-dependent D-stability criterion for the original discrete multiple time-delay singularly perturbed system under the composite state feedback control. If any one of the conditions of this criterion is fulfilled, D-stability of the original closed-loop system is thus investigated by establishing that of its corresponding slow and fast closed-loop subsystems. Finally, an efficient algorithm is proposed to obtain a less conservative D-stability bound of the singular perturbation parameter and to reduce the computation time.