We consider an autonomous system of a differential and a functional equation for one-dimensional motion of an object which attempts to regulate its distance from a given point by means of reflected signals. In a suitable, compact state space the forward initial value problem is well-posed. For certain configurations of the parameters involved we prove that there exist periodic orbits which are exponentially stable with asymptotic phase.
"Stable periodic motion of a system with state dependent delay." Differential Integral Equations 15 (8) 923 - 944, 2002.