März, Roswitha Practical Lyapunov stability criteria for differential algebraic equations. (English) Zbl 0801.34004 Kowalski, Jan Krzysztof (ed.) et al., Numerical analysis and mathematical modelling. Warszawa: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 29, 245-266 (1994). For quasilinear index 1 or index 2 differential algebraic equations (1) \(Ax'(t)+ g(x(t))= 0\) the authoress obtains stability criteria for an equilibrium point \(x^*\) in terms of the matrices \(A\), \(g'(x^*)\). As a by-product, she proves certain new solvability statements for index 3 equations (1) as well as for index 1 equations \(A(x(t))x'(t)+ g(x(t))= 0\), where the leading coefficient matrix \(A(x)\) has an \(x\)-dependent null space.For the entire collection see [Zbl 0790.00003]. Reviewer: W.Müller (Berlin) Cited in 9 Documents MSC: 34A09 Implicit ordinary differential equations, differential-algebraic equations 34D20 Stability of solutions to ordinary differential equations Keywords:quasilinear index 1 or index 2 differential algebraic equations; stability; solvability; index 3 PDFBibTeX XMLCite \textit{R. März}, Banach Cent. Publ. 29, 245--266 (1994; Zbl 0801.34004)