Effects of small delays on stability of singularly perturbed systems

A small delay in the feedback loop of a singularly perturbed system may destabilize it; however, without the delay, it is stable for all small enough values of a singular perturbation parameter ε. Sufficient and necessary conditions for preserving stability, for all small enough values of delay and ε, are obtained in two cases: in the case of delay proportional to ε and in the case of independent delay and ε. In the second case, the sufficient conditions are given in terms of an LMI. A delay-dependent LMI criterion for the stability of singularly perturbed differential-difference systems is derived.