Sufficiency-type stability and stabilization criteria for linear time-invariant systems with constant point delays (Q5894866)

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.