Non-existence of Periodic Solutions in a Class of Fourth Order Relay Control Systems

Abstract

This paper considers fourth order control systems with real, non-positive and distinct eigenvalues containing a relay with dead band and hysteresis. It is proved that if certain restrictions are imposed on the switching function parameters, the resultant system will have no periodic solutions. This result allows a relay system to be designed with only one restriction, namely that the switching hyper planes are parallel to certain easily defined hyper planes in state space.