A Linear Differential Inclusion for Contraction Analysis to Known Trajectories

• 成果类型: Article
• 署名作者: Harapanahalli, Akash; Coogan, Samuel
• 署名单位: University System of Georgia; Georgia Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3626266
• 发表日期: 2026
• 关键词: systems; criteria

摘要

Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a linear differential inclusion (LDI) encompassing the incremental behavior of the system. In this note, we use contraction tools to study the exponential stability of a system to a particular known trajectory, deriving a new LDI characterizing the error between arbitrary trajectories and this known trajectory. As with classical contraction analysis, this new inclusion is constructed via first partial derivatives of the system's vector field, and convergence rates are obtained with familiar tools: uniform bounding of the logarithmic norm and linear matrix inequality-based Lyapunov conditions. Our LDI is guaranteed to outperform a usual contraction analysis in two special circumstances: first, when the bound on the logarithmic norm arises from an interval overapproximation of the Jacobian matrix, and second, when the norm considered is the L-1 norm. Finally, wedemonstrate how the proposed approach strictly improves an existing framework for ellipsoidal reachable set computation.