A transformed Lure problem for sliding mode control and chattering reduction

1 March 1999

journal article
letter
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control

Vol. 44 (3) , 563-568
https://doi.org/10.1109/9.751351

Abstract

The sliding mode control problem is investigated here with the frequency domain approach. The authors show that the sliding mode control can be transformed into a Lure problem. With this formulation, it is shown that the conventional sliding mode control with a nonlinear sign function can only guarantee to make the overall system stable but not asymptotically stable. The authors also consider a practical situation where the sign nonlinearity may contain a hysteresis loop. For this situation, they show that even if the hysteresis loop is very small, there still exists a limit cycle. However, chattering phenomenon caused by the limit cycle behavior ran be eliminated by a certain class of nonlinearities.

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