Stabilization of solutions for nonlinear differential-algebraic equations

We consider a nonlinear controllable system of first order ordinary differential equations that is unsolved with respect to the derivative of the unknown vector function and identically degenerate in the domain. We obtain stabilizability conditions by linear approximation of systems with scalar input. We admit an arbitrarily high unsolvability index. Our analysis is done under assumptions that ensure the existence of a global structural form that separates “algebraic” and “differential” subsystems.