Direct assessment of transient singularity in differential-algebraic systems

Characterization of the stability boundary of differential-algebraic (DAE) systems is more complicated than for systems described by ordinary differential equations (ODEs). In addition to unstable equilibria and periodic orbits, algebraic singularity plays an important role in defining the stability boundary. This paper presents a Lyapunov-based method for direct assessment of transient singularity, thus enabling estimation of the region of state-space where the system model remains valid.