On the Lyapunov-Krasovskii functionals for stability analysis of linear delay systems. (English) Zbl 0952.34057
The authors consider the linear delay differential system
\[
\dot x(t)=Ax(t)+\sum_{i=1}^{r}A_{i}x(t-\tau_{i}) \tag{1}
\]
with the initial condition
\[
x(t_0+\theta)=\Phi(\theta),\quad \theta\in[-\tau,0]\quad (\tau=\max_{i=1,2,\dots ,r}\tau_{i}), \tag{2}
\]
where \(A, A_{i}\), \(i=1,2,\dots ,r\), are real constant matrices \(A_{i}\neq 0\), \(\tau_{i}\), \(i=1,2,\dots ,r\), are constant delays. Sufficient delay-independent/delay-dependent conditions are given that guarantee the asymptotic stability of the linear system (1)–(2). A Lyapunov-Krasovskii functional approach combined with linear matrix inequality techniques is used in the proof. The references of the paper contain more than fifty titles of books and papers.
Reviewer: J.Ohriska (Košice)
MSC:
34K20 | Stability theory of functional-differential equations |