The vehicle active suspension has drawn considerable attention due to its superiority in improving the vehicle dynamic performance. This paper investigates the nonfragile H control of delayed vehicle active suspension in a finite frequency range under nonstationary running. The control objective is to improve ride quality in a finite frequency band and ensure suspension constraints, and a quarter car model of the active suspension is established for a controller design. Then, the input delay, actuator uncertainty, and external disturbances are considered in the controller design. Moreover, a further generalization of the strict S-procedure is utilized to derive a sufficient condition in terms of linear matrix inequality (LMI) to capture performance in the concerned frequency range. Furthermore, a multi-objective controller is designed based on projection lemma in the framework of the solution of LMIs. A nonstationary road profile is established, and numerical simulations are also conducted to show the effectiveness and robustness of the proposed controller. Finally, experimental tests on a quarter-car test rig are implemented to examine the performance of the proposed controller for real applications.

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