Geometric Control of a Class of Nonlinear Descriptor Systems

This paper presents methods for the geometric control of a special class of nonlinear control systems. They are described by implicit differential equations, which are linear in their time derivatives. This type of control systems is also called descriptor system. The nonlinear and implicit system is converted to an exterior differential system. An algorithm is presented which transfers the latter to a special form that resembles an explicit control system. The investigations concerning accessibility and observability and the input-to-state and input-to-output linearization problems are based on this special form. Resuls and algorithms similar to those of the explicit case are obtained.