Consensus of Linear Discrete-Time Connected Autonomous Vehicle Systems With Time Delays and Multiplicative Noise

This paper investigates the consensus problem of a class of third-order discrete-time connected autonomous vehicle systems (CAVS) with constant delay and multiplicative noise. Based on the neighboring vehicle information, a novel cooperative look-ahead predictor-like control protocols are firstly designed for the CAVS to deal with time delay. Secondly, different from the existing literature that only the sufficient condition is obtained, the necessary and sufficient conditions in sense of the mean-square consensus are derived in this paper. The obtained results not only reveal an explicit relation among the system matrices, noise variance and time delay via an algebraic Riccati equation (ARE), but also amount the optimal control design problem to solving an eigenvalue problem (EVP). Furthermore, considering time delay and perturbations simultaneously, the necessary and sufficient conditions of string stability are further derived. Such conditions only depend on the controller parameters and the network weight. Finally, the validity of derived results is verified by some simulations.