Feedback linearization of nonlinear differential‐algebraic control systems

In this article, we study feedback linearization problems for nonlinear differential-algebraic control systems (DACSs). We consider two kinds of equivalences, namely, external equivalence, which is defined (locally) on the whole generalized state space, and internal locally maximal controlled invariant submanifold (i.e., set where solutions exist). define a notion called explicitation with driving variables, class ordinary differential equation (ODECSs) attaching to given DACS. Then give necessary sufficient conditions both show that linearizability DACS closely related involutivity distributions systems. Finally, illustrate results by an academic example constrained mechanical system.