Li, Miao; Gu, Xiao-Hui; Huang, Fa-Lun Robustness with respect to small time-varied delay for linear dynamical systems on Banach spaces. (English) Zbl 1069.34118 Stud. Math. 163, No. 3, 289-305 (2004). The authors consider the time-varied delay problem \[ x'(t)=Ax(t)+Bx(t-\tau(t)),\;t\geq 0,\quad x(\theta)=\xi(\theta),\;-r\leq\theta\leq 0,\tag{P} \] where \(A\) generates a \(C_0\)-semigroup on a Banach space \(X\), \(B\) is a closed densely defined linear operator on \(X\) and \(\tau\) is a continuous function.Under suitable assumptions, the authors prove that the problem \((P)\) has a unique solution, which is uniformly exponentially stable with small time-varied delay. Reviewer: Rodica Luca (Iaşi) MSC: 34K30 Functional-differential equations in abstract spaces 34K20 Stability theory of functional-differential equations 47D06 One-parameter semigroups and linear evolution equations 34K06 Linear functional-differential equations Keywords:\(C_0\)-semigroup; delay equations; robust stability PDFBibTeX XMLCite \textit{M. Li} et al., Stud. Math. 163, No. 3, 289--305 (2004; Zbl 1069.34118) Full Text: DOI