Annual Reviews in Control 47 (2019) 81–97 Contents lists available at ScienceDirect Annual Reviews in Control journal homepage: www.elsevier.com/locate/arcontrol String stability for vehicular platoon control: Definitions and analysis methods ∗ Shuo Feng a, Yi Zhang a, Shengbo Eben Li b, Zhong Cao b, Henry X. Liu c, Li Li a, a Department of Automation, Tsinghua University, Beijing, 10 0 084 China b Department of Automotive Engineering, Tsinghua University, Beijing 10 0 084, China c Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI 48109, United States a r t i c l e i n f o a b s t r a c t Article history: The platooning of connected and automated vehicles (CAVs) is expected to have a transformative im- Received 28 January 2019 pact on road transportation, e.g, enhancing highway safety, improving traffic efficiency, and reducing fuel Accepted 6 March 2019 consumption. One critical task of platoon control is to achieve string stability, for which various models Available online 16 March 2019 and methods had been proposed. However, different types of definitions and analysis methods for string Keywords: stability were proposed over the years and were not thoroughly compared. To fill these gaps, this pa- Stability per aims to clarify the relationship of ambiguous definitions and various analysis methods, providing a String stability rigorous foundation for future studies. A series of equivalences are summarized and discussed. The pros Vehicular platoon control and cons of different analysis methods and definitions are discussed, too. All these discussions provide Definition insights for practical selection of analyzing methods for vehicle platoons. Analysis method © 2019 Elsevier Ltd. All rights reserved. Contents 1. Introduction . 82 1.1. Motivation . 82 1.2. Scope and aim . 82 1.3. Contributions . 83 1.4. Structure . 83 2. Preliminaries. 83 3. Vehicular platoon control . 84 3.1. Platoon system description . 84 3.1.1. Node dynamics (ND) . 84 3.1.2. Information flow topology (IFT) . 84 3.1.3. Distributed controller (DC) . 84 3.1.4. Formation geometry (FG) . 84 3.1.5. Communication quality (CQ) . 84 3.1.6. Disturbances . 84 3.2. Control objectives . 84 3.3. Controller design methods . 85 4. A catalog of string stability definitions. 85 4.1. Original definition of string stability (OSS). 85 4.2. SFSS and its variants FSS, ESS, HTS . 85 4.3. TSS and ATSS . 86 ∗ Corresponding author. E-mail addresses: [email protected] (S. Feng), [email protected] (Y. Zhang), [email protected] (S.E. Li), [email protected] (Z. Cao), [email protected] (H.X. Liu), [email protected] (L. Li). https://doi.org/10.1016/j.arcontrol.2019.03.001 1367-5788/© 2019 Elsevier Ltd. All rights reserved. 82 S. Feng, Y. Zhang and S.E. Li et al. / Annual Reviews in Control 47 (2019) 81–97 4.4. LPSS, SLPSS and DSS . 86 5. Relations of string stability definitions . 87 5.1. Lyapunov string stability . 87 5.2. Input-to-output string stability . 87 5.3. Input-to-state string stability . 87 5.4. Relations of definitions . 87 5.5. Recommended definition. 88 6. Analysis methods . 89 6.1. z -domain analysis methods . 89 6.2. s -domain analysis methods . 89 6.3. Time-domain analysis methods . 90 6.4. Comparisons of analysis methods. 90 7. Alternative properties. 90 7.1. Studied platoon system . 90 7.2. Representative alternative properties . 91 7.3. Relations of the properties . 91 8. Discussions . 92 8.1. Longitudinal and lateral . ..