Exact linearization of nonlinear differential algebraic systems

Abstract

Describes an approach of exact linearization for single input nonlinear differential algebraic systems in general. The nonlinear differential algebraic control system being considered is not in state variable form. Some new definitions of M derivative and M bracket that are similar to the definitions of classic differential geometric theory and some related revised results are given. The definitions of M derivative and M bracket can be easily used to obtain the feedback control law of the nonlinear differential algebraic control systems. The conditions of exact linearization are shown. When given differential algebraic systems satisfy the proper conditions of exact linearization, the original differential algebraic control systems can be transformed into Brunovsky standard form with constraint algebraic equations.