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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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