Contraction Analysis of Nonlinear DAE Systems

• 成果类型: Article
• 署名作者: Nguyen, Hung D.; Vu, Thanh Long; Slotine, Jean-Jacques; Turitsyn, Konstantin
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2981348
• 发表日期: 2021
• 页码: 429-436
• 关键词: trajectory; Jacobian matrices; Power system stability; measurement; Mathematical model; Stability criteria; Contraction analysis; differential-algebraic equation (DAE); linear stability; Lyapunov analysis; transient stability

摘要

This article studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems. Such systems typically appear as a singular perturbation reduction of a multiple-time-scale differential system. In addition, a given DAE may result from the reduction of many synthetic differential systems. We show that an important property of a contracting DAE system is that the reduced system always contracts faster than any synthetic counterpart. At the same time, there always exists a synthetic system, whose contraction rate is arbitrarily close to that of the DAE. Synthetic systems are useful for the analysis of attraction basins of nonlinear DAE systems. As any rational DAE system can be represented in quadratic form, the Jacobian of the synthetic system can be made affine in the system variables. This allows for scalable techniques to construct attraction basin approximations, based on uniformly negative matrix measure conditions for the synthetic system Jacobian.