Robust Stability of Differential-Algebraic Equations under Parametric Uncertainty

This paper considers linear differential-algebraic equations (DAEs) representing a system of ordinary differential equations with an identically singular matrix at the derivative in the domain of its definition. The matrix coefficients of DAEs are assumed to depend on the uncertain parameters belonging to a given admissible set. For the parametric family under consideration, structural forms with separate differential and algebraic parts are built. As is demonstrated below, the robust stability of the DAE family is equivalent to the robust stability of its differential subsystem. For the structure of perturbations, sufficient conditions are established under which the separation of DAEs into the algebraic and differential components preserves the original type of functional dependence on the uncertain parameters. Sufficient conditions for robust stability are obtained by constructing a quadratic Lyapunov function.