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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

Citations:

Zbl 0916.93002
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