Ben Rzig, Ines; Kharrat, Thouraya Stability of perturbed delay homogeneous systems depending on a parameter. (English) Zbl 1499.34364 Kybernetika 57, No. 1, 141-159 (2021). The authors consider a nonlinear system with delay \[\dot x=f(x(t),x(t-\alpha(t)),\theta),\,\,\, t\ge 0,\] where \(f(0,0,\theta)=0\), \(f\) is a continuous homogeneous function locally Lipschitz with respect to the first two arguments, \(x\in R^n\) is the state vector, \(\alpha:[t_0,\infty)\to[0,\infty)\) is a continuous bounded function, \(\theta\in\Omega\) is a parameter and \(\Omega\subset R^d\) is a compact set. Uniform stability of trivial solution is studied by Lyapunov-Krasovskii approach. More general systems \[\dot x=f(x(t),x(t-\alpha(t)),\theta)+g(x(t),x(t-\alpha(t)),\theta)\] where \(f\) and \(g\) are homogeneous functions of different degrees and \[\dot x=f(x(t),x(t-\alpha(t)),\theta)+R(x(t),x(t-\alpha(t)),\theta)+P(x(t),\theta)\] under different assumptions on \(R\) and \(P\) are considered as well. Reviewer: Josef Diblík (Brno) MSC: 34K20 Stability theory of functional-differential equations Keywords:nonlinear homogeneous system; varying delay; stability; Lyapunov function; Razumikhin theorem PDFBibTeX XMLCite \textit{I. Ben Rzig} and \textit{T. Kharrat}, Kybernetika 57, No. 1, 141--159 (2021; Zbl 1499.34364) Full Text: DOI Link