Robust stability for a class of two-time-scale time-delay neutral systems

In this paper, the robust stability problem for a class of uncertain two-time-scale neutral systems subject to unstructured perturbations is investigated. The properties of H_∞-norm are used throughout this paper to derive the robust stability criterion. A frequency-domain delay-dependent criterion for the asymptotic stability of the slow neutral subsystem and the fast subsystem of the nominal two-time-scale neutral system is first presented. Under the condition that the slow neutral and fast subsystems of the nominal system are both asymptotically stable, we then propose the allowable bounds for the system uncertainties such that the slow neutral subsystem and the fast subsystem of the original uncertain two-time scale neutral system are both asymptotically stable. Finally, a stability bound ε^* of the small parameter ε is given such that the original uncertain two-time scale neutral system is asymptotically stable for any ε ∈ (0, ε^*).