The order reduction and robust D-stability analysis of discrete uncertain time-delay systems by time-scale separation

In this paper, the robust D-stability problem for discrete uncertain multiple time-delay systems is examined on the basis of their such reduced-order models (the slow and fast subsystems), which are obtained by time-scale separation method. Under the condition that the slow and fast subsystems of the nominal system are both -D(a,r)-stable, a D-stability criterion for the slow and fast subsystem of the original uncertain system is first derived. A delay-dependent criterion in terms of spectral radius is then proposed to guarantee the robust D-stability of the original uncertain system subject to structured perturbations. Moreover, the criterion for the robust asymptotic stability of the system subject to structured perturbations can be obtained from the proposed robust D-stability criterion. A numerical example is provided to illustrate our main results.