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)].
Reviewer: Michael I.Gil’ (Beer-Sheva)