## On delay-dependent stability and decay estimate for uncertain systems with time-varying delay.(English)Zbl 0951.93059

The authors consider the system described by the equation $\dot x=(A+\Delta A(t))x(t)+(A_1+\Delta A_1(t))x(t-\tau (t)).$ It is assumed that with induced matrix 2-norm $\|\Delta A(t)\|\leq \alpha (t\geq 0)$ and $\|\Delta A_1(t)\|\leq \alpha_1 (t\geq 0).$ Explicit stability conditions are established. The main result of the paper is similar to the particular case of Theorem 9.7.1 from the book by M. I. Gil’ [Stability of finite and infinite dimensional systems, Kluwer Academic Publishers, Boston etc. (1998; Zbl 0916.93002)].

### MSC:

 93D09 Robust stability 34K20 Stability theory of functional-differential equations

### Keywords:

linear delay systems; robust stability

Zbl 0916.93002
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