String stability analysis of a vehicle platoon with communication range 2 using the two-dimensional induced operator norm

Vehicle strings can be modelled as continuous-discrete 2D systems. However, every such 2D system includes a structural nonessential singularity on the stability boundary and special care is needed to analyse BIBO stability of the system. A unidirectional vehicle string with communication range 2 is analysed and simulated.

[1]  Leonard T. Bruton,et al.  Using nonessential singularities of the second kind in two-dimensional filter design , 1989 .

[2]  S. Treitel,et al.  Stability and synthesis of two-dimensional recursive filters , 1972 .

[3]  H. Reddy,et al.  Study of the BIBO stability of 2-D recursive digital filters in the presence of nonessential singularities of the second-kind-Analog approach , 1987 .

[4]  Diana Yanakiev,et al.  A SIMPLIFIED FRAMEWORK FOR STRING STABILITY ANALYSIS OF AUTOMATED VEHICLES , 1998 .

[5]  H.C. Reddy,et al.  A simpler test set for two-variable very strict Hurwitz polynomials , 1986, Proceedings of the IEEE.

[6]  P. Barooah,et al.  Error Amplification and Disturbance Propagation in Vehicle Strings with Decentralized Linear Control , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[7]  Glenn Vinnicombe,et al.  Scalable Decentralized Robust Stability Certificates for Networks of Interconnected Heterogeneous Dynamical Systems , 2006, IEEE Transactions on Automatic Control.

[8]  K. Chu Decentralized Control of High-Speed Vehicular Strings , 1974 .

[9]  João Pedro Hespanha,et al.  Mistuning-Based Control Design to Improve Closed-Loop Stability Margin of Vehicular Platoons , 2008, IEEE Transactions on Automatic Control.

[10]  H. Ansell On Certain Two-Variable Generalizations of Circuit Theory, with Applications to Networks of Transmission Lines and Lumped Reactances , 1964 .

[11]  Srdjan S. Stankovic,et al.  Decentralized overlapping control of a platoon of vehicles , 2000, IEEE Trans. Control. Syst. Technol..

[12]  M. Athans,et al.  On the optimal error regulation of a string of moving vehicles , 1966 .

[13]  Charles A. Desoer,et al.  Longitudinal Control of a Platoon of Vehicles , 1990, 1990 American Control Conference.

[14]  Panajotis Agathoklis,et al.  Algebraic necessary and sufficient conditions for the very strict Hurwitz property of a 2-D polynomial , 1991, Multidimens. Syst. Signal Process..

[15]  Tuo-Yeong Lee Henstock-Kurzweil Integration on Euclidean Spaces , 2011 .

[16]  R. Roesser A discrete state-space model for linear image processing , 1975 .

[17]  Peter Seiler,et al.  Disturbance propagation in vehicle strings , 2004, IEEE Transactions on Automatic Control.

[18]  Petros A. Ioannou,et al.  Automatic Vehicle-Following , 1992, 1992 American Control Conference.

[19]  Richard H. Middleton,et al.  Two-dimensional frequency domain analysis of string stability , 2012, 2012 2nd Australian Control Conference.

[20]  Panajotis Agathoklis,et al.  On the Positive Definite Solutions to the 2-D Continuous-time Lyapunov Equation , 1997, Multidimens. Syst. Signal Process..