The zero dynamics of a nonlinear system: From the origin to the latest progresses of a long successful story

The concept of zero dynamics of a nonlinear system was introduced about thirty years ago as nonlinear analogue of the concept of transmission zero of the transfer function of a system. This paper reviews a few historical landmarks in the development of this concept and then addresses some current challenging issues, such as the development of global and coordinate free version of a standard output-feedback design paradigm, the analysis of problems of stabilization and tracking in the presence of unstable zero dynamics, and extensions to multivariable systems.