Robust stability of differential-algebraic equations with an arbitrary unsolvability index

Abstract

Consideration was given to the linear stationary systems of differential-algebraic equations with an arbitrarily high unsolvability index. Conditions were established guaranteeing the internal structure of the system at hand against the internal structural modifications caused by the perturbations of the matrix coefficients. Under the assumptions of structural persistence, the sufficient conditions for robust stability were obtained, and the values of real stability radii were given.