, We discuss the differences of the two explicitation procedure in Remark 3.2.5 of Chapter 3 for linear DAE systems and show in Theorem 4.3.27 that a nonlinear DAE ? = (E, F ) admits an explicitation without driving variables if and only if the distribution defined by ker E(x) is of constant rank and involutive, which also explains when ? is externally equivalent to a SE DAE ? se . 4. Connections between DAE and ODE systems. The connections between the two classes of systems are built up depending on the results that the external (feedback) equivalence for DAE systems is a true counterpart of the system (feedback) equivalence (the (extended) Morse equivalence for the linear case) for ODE systems, order to "explicitate" the "implicit" DAE systems and connect DAE systems with ODE systems, we propose two kinds of explicitation procedures, i.e., the explicitation with driving variables (or (Q, v)-explicitation) and without driving variables (or (Q, P )-explicitation)

, 1) to simplify the construction of the Morse normal form MNF (Proposition 3.3.2) of classical ODE control systems and then the MTF and MNF are generalized, respectively, to the extended Morse triangular form EMTF (Theorem 3.3.4) and the extended Morse normal form EMNF (Theorem 3.3.5) for ODE control systems with two kinds of inputs

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