Robust stability for a class of uncertain singularly perturbed systems with multiple time delays

In this paper, the works on the stability problem for singularly perturbed systems are extended to include the factors of uncertainties and time delay s, which often cause the instability of the systems. The properties of H in finity (-)norm are used throughout this paper to derive the robust stabilit y criterion. A frequency-domain sufficient condition for the asymptotic sta bility of the slow subsystem (reduced-order model) and the fast subsystem o f the nominal system is first presented. Under the condition that the slow and fast subsystems of the nominal system are both asymptotically stable, w e then propose the allowable bounds for the system uncertainties such that the slow and the fast subsystems of the original uncertain system is asympt otically stable. Finally, an upper bound epsilon* of the singular perturbat ion parameter epsilon is given such that the original uncertain System is a symptotically stable for any epsilon is an element of=(0, epsilon*). A nume rical example is provided to illustrate our main results.