Semi-active skyhook systems can chatter between the on and off states, and Fig. 3 shows typical time histories of the damping and spring forces when chatter occurs. Since a semi-active damper system is energetically passive, the chatter depends totally on the instantaneous states of the system. Donald and Mehrnaz studied the occurrence of chatter for on–off skyhook control and suggested a modified logic to cure it [19]. For the semi-active skyhook control, switches due to changes in the sign of the mass velocity, ’ x; are defined as ‘‘’ x switches’’, while those due to changes in the sign of ’ x  ’ x0 are called ‘‘’ x  ’ x0 switches’’. Recalling the form of damping forces for the on– off and continuous skyhook dampers in Eqs. (4) and (8), it is noted that only ’ x switches are important with respect to the potential of chatter for the on–off skyhook control and ’ x  ’ x0 switches are important for the continuous skyhook control. This is because for the on–off skyhook control, ’ x switches can be associated with large relative velocity, ’ x  ’ x0; and thus large damping forces, while ’ x  ’ x0 switches are always associated with small damping forces. Conversely, for continuous skyhook control, ’ x  ’ x0 switches can be associated with large damping forces. Also, chatter can only occur if the damper and spring force are in opposition, and if the on-state damping force is of larger magnitude than the instantaneous spring force. If the damping force is not greater than the spring force, then the damper does not change the direction of the acceleration and does not initiate chatter [19].