Stability region for quasi-linear differential-algebraic equations

This paper investigates the stability region for a class of quasi-linear differential–algebraic equations. We focus on the stability region associated with a hyperbolic equilibrium point under the assumption that the system is strangeness-free (i.e. of differentiation index 1) at that point. First, we present detailed characterizations of the structure of the stability boundary for two separate cases, distinguished by whether or not singular points are taken into account. Based on these insights, we then develop a practical algorithm for computing the stability region. Finally, two numerical examples are included to illustrate and validate the theoretical results.