On the optimality of hysteresis operators in signal processing and communication systems

This paper demonstrates that hysteresis operators are the optimal estimators for a large class of estimation and decision problems. This class of problems arises whenever a cost is associated with actions needed to process changes in the estimates or decisions. A simple example related to least-squares estimation is used to illustrate and motivate the developments in this paper. Subsequently, the problem of mean-square estimation with minimal cost of actions is investigated. These results provide a justification for the use of hysteresis in many practical signal processing and communication applications. r 2005 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.