Stability Analysis of Connected Vehicle Platoons With Markovian Packet Losses

This article focuses on discussing the effects of inter-vehicular communication on the performance of platoon control. Different from the existing results established under a critical assumption that the fading channels are independent, this paper models the inter-vehicular communication as Markovian packet loss channel which can capture the temporal interdependencies of packet losses. Our aim is to decide whether there exists a distributed controller such that the underlying vehicle platoon can achieve mean square stability (MSS) over Markovian packet loss channels. First, for the scenario with identical Markovian packet losses, we begin by deriving a necessary and sufficient condition for the platoon MSS, which is established by utilizing the stability principles of Markov jump linear systems. Additionally, we propose a numerically verifiable criterion for MSS, which can be validated through the feasibility of linear matrix inequalities (LMIs). Furthermore, based on the modified Riccati inequality (MRI), we provide an analytical sufficient condition that ensures MSS for vehicle platoons. This condition is expressed in terms of the information flow topology (IFT) and the statistical parameters of Markov channels. Second, for the case with nonidentical packet dropouts, we introduce a Markovian loss channel based switching (MLCBS) model. Building upon this model, we further propose a sufficient conditon related to IFT and the transition probability matrix, and a distributed controller that is not only easy to implement but also enables the achievement of MSS for vehicle platoons with nonidentical packet dropouts. Ultimately, numerical experiments are performed to validate the obtained outcomes.