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 delays, which often cause the instability of the systems. The properties of ∞ H -norm are used throughout this paper to derive the robust stability criterion. A frequency-domain sufficient condition for the asymptotic stability of the slow subsystem (reduced-order model) and the fast subsystem of the nominal system is first presented. Under the condition that the slow 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 and the fast subsystems of the original uncertain system is asymptotically stable. Finally, an upper bound ∗ ε of the singular perturbation parameter ε is given such that the original uncertain system is asymptotically stable for any ( ) ∗ ∈ ε ε , 0 . A numerical example is provided to illustrate our main results.