This article presents a cross-layer framework that integrates realistic
vehicle-to-network-to-vehicle (V2N2V) delay characterization with a rigorous
stability analysis of automated vehicle steering control. Both constant and
network-induced time-varying delays modeled via deterministic bounds are
addressed. For constant delays, delay-independent stability regions within the
controller gain space are analytically derived. For time-varying delays with
stochastic network origins, modeled using deterministic bounds, a refined
Lyapunov–Krasovskii functional (LKF) incorporating augmented single- and
double-integral terms is constructed. To establish delay-dependent linear matrix
inequality (LMI) conditions, a reciprocally convex combination approach is
employed to handle the delay interval partitioning, and the second-order
Bessel–Legendre inequality is applied to tighten the integral quadratic bounds.
The resulting LMI conditions explicitly capture the coupled effects of delay
magnitude, delay variation rate, and control gains on closed-loop stability.
Simulations of a lane-keeping scenario confirm that the predicted stability
boundaries accurately match the closed-loop system behavior. Notably,
incorporating a realistic time-varying V2N2V delay profile into the controller
design reduces the lateral-state root-mean-square error (RMSE) by over 54% and
decreases the settling time by a factor of 10 compared to designs relying on an
average-delay assumption. However, high packet loss rates are shown to still
induce residual oscillations due to information scarcity. Ultimately, these
results elucidate delay-induced instability mechanisms and provide practical
guidelines for designing delay-robust steering controllers for connected and
automated vehicles.
