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Effects of small delays on stability of singularly perturbed systems. (English) Zbl 1014.93025
The author gives an example of a finite-dimensional singularly perturbed linear system that may be destabilized by introduction of a small delay in the feedback loop. Necessary and sufficient conditions for preserving stability, for all small enough values of delay and of the singular perturbation parameter $$\varepsilon$$, are obtained in two cases: in the case of delay proportional to $$\varepsilon$$ and in the case of independent delay and $$\varepsilon$$.
In the second case, the sufficient conditions are given in terms of a LMI. A delay-dependent LMI criterion for the stability of singularly perturbed differential-difference systems is derived.

##### MSC:
 93C70 Time-scale analysis and singular perturbations in control/observation systems 93D09 Robust stability 93C23 Control/observation systems governed by functional-differential equations 15A39 Linear inequalities of matrices
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