Robust LMI-based control for stability, safety and efficiency of CACC platoons considering actuation and communication delays

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.