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A transformed Lure problem for sliding mode control and chattering reduction

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2 Author(s)
Ching-Yei Chung, S. ; Dept. of Autom. Control Eng., Feng Chia Univ., Taichung, Taiwan ; Chun-Liang Lin

The sliding mode control problem is investigated 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 can be eliminated by a certain class of nonlinearities

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Automatic Control, IEEE Transactions on  (Volume:44 ,  Issue: 3 )