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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.

MSC:
 34K20 Stability theory of functional-differential equations
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