Cooperative adaptive cruise control (CACC) can efficiently improve platoon performance, but its practical deployment is strongly affected by actuation and communication delays. To this end, this paper proposes a mixed-norms synthesis for delay-aware CACC that simultaneously ensures performance objectives. The control synthesis is formulated as an optimization problem for a time-delay system, where the performance requirement is transformed into a set of convex linear matrix inequalities (LMIs). Through convex optimization, the feedback and feedforward gains are jointly solved to suppress disturbance propagation along the platoon, maintain safe inter-vehicle spacing, and enhance overall traffic efficiency. In contrast to the empirical tuning approach, the proposed method provides a theoretically grounded and computationally efficient synthesis procedure. An innovation of this work lies in explicitly modeling and mitigating the impact of actuation and communication delays on the closed-loop platoon dynamics. The design enforces local and string stability through H-infinite attenuation channels, and improves transient performance through H-2 average-energy shaping. Comprehensive simulations are conducted in both frequency and time domains. Under the nominal delay setting, the proposed controller achieves a minimum feasible headway of 0.53 s while preserving practical string stability and bounded spacing errors. In the acceleration scenario, it further achieves reductions of 22.2% and 37.4% over the benchmark in terms of peak and accumulated spacing errors, respectively. In the mixed-frequency NGSIM scenario, the proposed controller reduces the feasible headway by at least 10.0% compared with the benchmarks.It also yields the lowest accumulated spacing error, reducing it by at least 9.7%, and lowers the peak spacing error by at least 24.1% among the comparable benchmark cases. These results show that the proposed method achieves a balanced overall advantage under realistic traffic excitation. Therefore, the proposed method provides an effective delay compensation solution for CACC platoons, jointly enhancing string stability, spacing safety, and traffic efficiency.