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Mechatronic subsystems have been extensively developed in automotive applications as they increase performance compared to passive components. The Hydractive CRONE suspension based on fractional differentiation is presented as a hybrid system undergoing an infinite sequence of autonomous switchings. The modelling and operation of Hydractive CRONE suspension as a hybrid system are presented. The stability of Hydractive CRONE suspension is demonstrated using the maximum principle extended to hybrid systems. Finally, comfort mode synthesis is proposed using the third generation CRONE control system design.