Oscillations and transfer properties of relay feedback systems with time-delay linear plants

Oscillations and transfer properties of relay feedback systems with linear plants having a dead time (time delay) are considered. Poincare maps are found explicitly in terms of the system parameters. The oscillatory and transfer properties are presented in the format of the locus of a perturbed relay system (LPRS), which represents the continuum of all possible periodic solutions and transfer properties of the system with a given linear plant. Conditions of local orbital asymptotic stability are found in terms of the system parameters. The proposed approach is illustrated by examples.