The paper presents a new controller design approach for a four-degrees-of-freedom half-car suspension model considering the time delay in the control input. The time delay for the control input is assumed to be uncertain time invariant within a known constant bound. The ride comfort performance of the suspension system is optimized by using the H∞ norm to measure the body accelerations (including both the heaving and the pitching motions), while the tyre deflections and the suspension rattle spaces are constrained by their peak response values in time domain using the generalized H2 (GH2) norm (energy-to-peak) performance. Then, a constrained delay-dependent H∞ state feedback controller is designed to realize the ride comfort, road holding and stroke limitation performance to prescribed level in spite of the existence of a time delay in control input. The design approach is formulated in terms of the feasibility of certain delay-dependent matrix inequalities. A numerical example is used to illustrate the effectiveness of the approach. It shows that the designed controller can keep the stability of the closed-loop system while improving the performance on ride comfort, keeping suspension strokes within given bounds, and ensuring firm contact of wheels to road even with the existence of a time delay in the control input to some extent.
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