Frequency criterion of boundedness of solutions to phase systems with delay (Q1902795)

For a system of the type \(dx/dt = Ax + b \varphi (t, \sigma (t - \tau (t)))\), \(\sigma = c^Tx\), where \(\varphi (t, \sigma)\) is periodic with respect to \(\sigma\) and satisfies an inequality \(\mu_1 \leq \varphi (t, \sigma)/ \sigma \leq \mu_2\) with constants \(\mu_1 < 0 < \mu_2\) and the delay \(\tau (t)\) is a continuous function of \(t\) with \(0 \leq \tau (t) \leq T\), \(T\) some positive constant, the author presents a frequency domain criterion for boundedness of all solutions.