Geometric analysis of nonlinear differential-algebraic equations via nonlinear control theory

For nonlinear differential-algebraic equations (DAEs), we define two kinds of equivalences, namely, the external and internal equivalence. Roughly speaking, word “external” means that consider a DAE (locally) everywhere “internal” on its maximal invariant submanifold (i.e., where solutions exist) only. First, revise geometric reduction method in DAEs solution theory formulate an implementable algorithm to realize method. Then procedure called explicitation with driving variables is proposed connect control systems show system can be reduced under some involutivity conditions. Finally, due explicitation, use notions from derive generalizations Weierstrass form.