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On Impasse Points of Quasilinear Differential Algebraic Equations

Abstract : This paper presents a mathematical characterization of the impasse points of quasilinear DAE's A(x) = G(x), where then A(x) is a nxn matrix having constant but not full r<n in the domain of interest. We show that a reduction procedure permits to reduce the DAE to a quasilinear ODE Al(xi)xi'=G1(xi) Rr and that impasse points correspond to special singularities of the reduced ODE. Impasse points of higher index DAE's can also be defined; the only difference is that the above reduction procedure takes more than one step.