Distributed Consensus Control for Connected Vehicle Platoon with Markovian Switching Topology and Heterogeneous Time-Varying Delays

Reliable cooperative control of connected vehicle platoons remains challenging when stochastic communication-topology variations coexist with heterogeneous time-varying transmission delays. This study investigates a distributed consensus control problem for connected vehicle platoons subject to Markovian switching topologies and heterogeneous time-varying inter-vehicle communication delays. A third-order longitudinal vehicle model with powertrain inertial lag is combined with a continuous-time Markov chain (CTMC) to describe randomly switching communication topologies. A distributed control protocol incorporating the constant time headway policy, full velocity difference car-following behavior, and leader-pinning information is formulated, while link-dependent time-varying delays are embedded in the closed-loop error system. Based on a mode-dependent Lyapunov–Krasovskii functional, Jensen’s integral inequality, and the Schur complement, sufficient linear matrix inequality (LMI) conditions are derived for mean-square asymptotic stability of the nominal delayed system; the LMI is feasible at τ¯ℓ=0.10 s and μℓ=0.04, remains feasible at 0.30 s, and becomes infeasible at 0.375 s. An input-to-state stability (ISS) corollary extends the result to bounded time-varying leader acceleration, showing that tracking errors remain bounded during dynamic EUDC phases and converge when the leader acceleration and its derivative vanish. Using the same Lyapunov–Krasovskii certificate, a mean-square L∞ bounded-propagation result is further established; this result characterizes uniform-in-vehicle error bounds and does not assert strict non-amplification. Numerical simulations under the Extra-Urban Driving Cycle (EUDC) show that the follower vehicles maintain cooperative tracking under topology switching and bounded communication delays, with position, velocity, and acceleration errors remaining bounded during the dynamic phases and converging as the leader acceleration vanishes. In the EUDC simulation, the largest leader-relative position error is approximately −60.75 m for Vehicle 10 at t≈380 s, the maximum adjacent local spacing-error peak ratio is 2.32, and the position error returns below 1 m by t≈400.8 s. The minimum inter-vehicle gap is 5.87 m and the minimum safety margin after the initial 10 s is 0.84, with all safety-margin indices remaining positive; these results indicate that the proposed framework maintains platoon coordination and car-following safety under stochastic communication uncertainties.