Stability criteria for nonlinear fully implicit differential algebraic systems

Overview & Synopsis

The goal of this note is to contribute to the qualitative theory of differentialalgebraic systems by providing new asymptotic stability criteria for a class of nonlinear, fully implicit DAEs with tractability index two. Topics covered includes, State space analysis of differentialalgebraic equations, Properly formulated DAEs with tractability index 2, The state space form, Index reduction via differentiation, Stability criteria for differentialalgebraic systems, Asymptotic stability of periodic solutions, Lyapunovs direct method regarding DAEs.