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Fast switches in relay feedback systems
 AUTOMATICA 35 (1999) 539—552
, 1999
"... Relays are common in automatic control systems. Even linear systems with relay feedback are, however, far from fully understood. New results are given about the behavior of these systems via a statespace approach. It is proved that there exist multiple fast switches if and only if the sign of the ..."
Abstract

Cited by 29 (6 self)
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Relays are common in automatic control systems. Even linear systems with relay feedback are, however, far from fully understood. New results are given about the behavior of these systems via a statespace approach. It is proved that there exist multiple fast switches if and only if the sign of the first nonvanishing Markov parameter of the linear system is positive. Fast switches are shown to occur as part of stable limit cycles. An analysis is developed for these limit cycles that illustrates how they can be predicted.
Global Analysis Of ThirdOrder Relay Feedback Systems
, 1996
"... Relays are common in automatic control systems. It is wellknown 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 thirdorder systems. It is shown that there exist systems giving ..."
Abstract

Cited by 3 (1 self)
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Relays are common in automatic control systems. It is wellknown 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 thirdorder 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.