Dynamics of constrained differential delay equations (Q1841956)

A class of first-order differential delay equations with piecewise-affine right-hand sides is studied. These equations have a control theory application where the phase variable represents the speed of a motor which is trying to adjust a prescribed (possibly time dependent) target speed \(f\). Assuming that \(f\) is periodic with amplitude \(A\) and period \(T\), a simple pure delay form is mainly considered. For \(A=0\) or A large, the existence of periodic solutions is shown. A numerical approach, based on piecewise-polynomial structure is also discussed briefly. Numerical results are then presented, including simulations for intermediate values of \(A\) where the considered analytical results do not apply.