Stability margin of a cyclic platoon with a single distinct vehicle

초록

This paper evaluates the stability margin (SM) of heterogeneous ring vehicular networks containing a single distinct vehicle. While robustness analysis of string networks has been extensively studied using metrics such as L2-string stability and H infinity norms, ring networks-arising in closed traffic loops, satellite constellations, and circular autonomous formations-have received comparatively less attention. Moreover, existing studies of ring topologies typically assume homogeneous dynamics and do not provide general, analytically tractable robustness measures for heterogeneous systems. To address this gap, we characterize robustness using the minimum singular value (MSV) of the network transfer function. The main findings are threefold. First, two distinct SMs are introduced, which respectively quantify the allowable additive and multiplicative uncertainties that preserve closed-loop stability. Second, these margins admit compact characterizations in terms of vehicle parameters, revealing how heterogeneity in a single vehicle degrades network robustness. Third, tight analytical bounds on the SMs are derived by evaluating the frequency response of a scalar transfer function, avoiding the need to compute MSVs of large frequency-dependent matrices whose dimension grows with the number of vehicles. Numerical results demonstrate that the proposed SM captures robustness properties not revealed by H infinity- or string-stability-based metrics, highlighting its significance for heterogeneous ring networks.

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