Stabilization of differential-algebraic systems with Lipschitz nonlinearities via feedback decomposition

The stabilization problem for differential-algebraic systems with Lipschitz nonlinearities is addressed. The proposed stabilization technique is based on the interpretation of differential-algebraic systems as the feedback interconnection of a linear system and an algebraic system. In this framework the algebraic variable and the nonlinearities can be treated as external disturbances acting on the linear system. A direct consequence of this approach is that the control problem reduces to a classical disturbance attenuation problem with internal stability. The application of the proposed theory to linear differential-algebraic systems recovers classical results. A simple example validates the technique.