Stability of an interval family of differential-algebraic equations with variable coefficients (Q2314449)

This paper is concerned with the asymptotic stability of the following interval family of linear Differential-Algebraic Equations (DAEs) \[ \left( A(t) + \Delta_A(t) \right) x'(t) + \left( B(t) + \Delta_B(t) \right) x(t) = 0, \quad t\in [0,\infty) \] where \(x(t)\) is an unknown vector-valued function, \(\Delta_A\), \(\Delta_B\) are uncertainty matrices-valued functions. It is well-known, that the most important characteristic of differential-algebraic equations is the index concept, which measures the complexity of the internal structure of a system. In this research, the authors provide sufficient conditions for the preservation of an index, followed by sufficient and necessary robust stability conditions. Furthermore, a variable rank of matrix coefficients and an arbitrary high index are allowed.