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Sufficiency-type stability and stabilization criteria for linear time-invariant systems with constant point delays. (English) Zbl 1067.34078
The following linear system is considered \[ \dot{x}(t)=A_{0}x(t)+\sum_{k=1}^{r}A_{k}x(t-\tau_{k}),\;t\geq 0\;, \] where \(\tau_{k},k=1,\dots,r\), are unknown delays.
Criteria for \(\alpha\)-stability (anti-stability) local in the delays and \(\varepsilon\)-stability independent of the delays are established. Moreover, questions on robust stability and closed-loop stabilization are discussed.

MSC:
34K20 Stability theory of functional-differential equations
93D09 Robust stability
93D15 Stabilization of systems by feedback
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