Stability of an Interval Family of Differential-Algebraic Equations with Variable Coefficients

Abstract

We consider a linear nonstationary system of ordinary differential equations with interval coefficients which is not solvable with respect to the derivative of the unknown vector-valued function for any matrix coefficients in a given interval family. We obtain conditions sufficient for the preservation of the internal structure of the system. Under conditions guaranteeing the structure preservation, we obtain sufficient and necessary robust stability conditions. A variable rank of matrix coefficients and an arbitrary high unsolvability index are allowed.