Contraction Analysis of Nonlinear DAE Systems

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