Stability Analysis With LMI Based Distributed H∞ Controller for Vehicle Platooning Under Random Multiple Packet Drops

This paper proposes a discrete time distributed state feedback controller design strategy for a homogenous vehicle platoon system with undirected network topology which is resilient to both external disturbances and random consecutive network packet drop. The system incorporates a distributed state feedback controller design by satisfying bounded $H_{\infty }$ norm using Lyapunov-Krasovskii based linear matrix inequality (LMI) approach that ensures internal stability and performance. The effect of packet drops on internal stability in terms of stability margin are studied for a homogenous vehicle platoon system with undirected network topology and external disturbance. The variation of stability margin, representing absolute value of least stable close-loop pole, is also studied for two common undirected network topologies for vehicle platooning, i.e., bidirectional predecessor following (BPF) and bidirectional predecessor leader following (BPLF) topologies by varying platoon members, packet drop rates with number of contiguous packets dropped. Results demonstrate that the control strategy best satisfies the requirement of maintaining a desired inter-vehicular distance with constant spacing policy and leader trajectory using two network topologies: BPF and BPLF. We show how these topologies are robust in terms of ensuring internal stability and performance to maintain cooperative motion of vehicle platoon system with different number of followers, random multiple consecutive packet drops and external disturbance.