Global Analysis of Third-Order Relay Feedback Systems*

Abstract Relays are common in automatic control systems. It is well-known that a linear dynamical system under relay feedback can give complex oscillations. In this paper it is proved that several of these phenomena can actually be captured by third-order systems. It is shown that there exist systems giving arbitrarily fast relay switches similar to sliding modes. A novel method for analyzing linear dynamical systems under relay feedback is also introduced. Trajectories for a class of third order systems are shown to converge in a certain sense.