Lyapunov regularity of linear differential algebraic equations of index 1
The paper continues the work of both authors to extend the qualitative ODE theory to DAEs (see [Acta Math. Vietnam. 28, No. 1, 73--88 (2003; Zbl 1048.34089)]). The concept of Lyapunov regularity (Perron's theorem) of ODEs is extended to tractable index-1 DAEs. The necessary basics of the tractability index of DAEs and the Lyapunov exponent of functions are introduced. Lyapunov regularity of index-1 DAEs is defined and the relation of that definition to the corresponding ODE is discussed. It is shown that this regularity concept is invariant under regular transformations of the unknowns and does not depend on the choice of the projectors to represent the corresponding ODE.
scientific article; zbMATH DE number 2113028