Stability issues in regular and noncritical singular DAEs
The author surveys results on the stability of equilibria in both regular and singular differential algebraic equations. After a brief review of some basic notions concerning differential-algebraic equations including singularity induced bifurcations, he discusses the regular case: first, linear systems are studied using matrix pencils, then the theory is extended to semiexplicit and quasilinear systems. In the treatment of singular equations, the author distinguishes between stationary and nonstationary problems. In the latter case, he analyses index 0 and index 1 equations. The main point is to prove the existence of a submanifold, transversal to the singular locus, on which the dynamics is well-defined. Finally, the stationary case is studied for index 0 equations. Again, matrix pencils are the basic tools, although new complications arise since the relevant pencils are singular.
scientific article; zbMATH DE number 1879597