An analysis on the stability of a state dependent delay differential equation (Q317899)

The authors first establish the existence and uniqueness of solutions of differential equations with state-dependent delay term of the form NEWLINENEWLINE\[NEWLINEu'(t)=-A_0u(t)-A_1u(t-\tau(u(t))),NEWLINE\]NEWLINE where \(A_0\), \(A_1\in\mathbb R\) and \(\tau(u(t))>0\) for all \(t\in\mathbb R^+\). Stability criteria in terms of the parameters of the equation are subsequently obtained based on the boundedness of the delay as well as some restrictions on the positivity of the delay.