On the stability of solutions of autonomous index-1 tractable and quasilinear index-2 tractable DAEs (Q1327403)

The authoress presents sufficient conditions for asymptotic stability of autonomous index 1 differential algebraic equations \(f(x'(s),x(t))= 0\) in terms of the eigenvalues of the matrix pencil \(\{A,B\}\), where \(A= f'y(0,x_ 0)\), \(B= f'x(0,x_ 0)\), \(x_ 0\) a stationary solution, and for quasilinear index 2 differential algebraic equations \(Ax'(t)+ g(x(t))= 0\) with additional regularizing terms.