A Survey on Linearization of Nonlinear Systems

Linearization is one of the most powerful tools in control of nonlinear systems. It has obtained various applications in aircraft pilot control, safety control of power systems, chemical reactor control, economical system, biological system, robot control etc. This survey outlines the long history and the recent development of linearization, including different techniques and useful results. We first recall the development of the linearization from approximated one to exact one. Poincare's linearization is reviewed. The necessary and sufficient conditions and algorithms of the state feedback linearization are mentioned. Then various kinds of linearizations are surveyed, which includes the global linearization, full linearization, input-output linearization, non-regular feedback linearization. Partial linearization and its relationship with relative degrees are sequentially discussed. Some other linearization techniques such as dynamic feedback linearization, approximate linearization, Carleman Linearization etc. are also briefly introduced. The paper is expected to provide a complete picture of linearization: its past, present and key issues for further investigation.