Sampled-Data Models for Nonlinear Systems via the Taylor-Lie Series and Multirate Input

Abstract: It is well-known that the existence of unstable zero dynamics is recognized as a major barrier in many control problems. This paper investigates an approximate sampled-data model for nonlinear systems by the use of multirate input and hold such as a generalized sample hold function (GSHF), and further analyzes the sampling zero dynamics of the sampled-data model to show a condition which assures the stability of the sampling zero dynamics of the model. The results presented here show how sampling zero dynamics of the obtained model can be arbitrarily placed. In a word, the stability of the sampling zero dynamics is definitely improved compared with a zero-order hold (ZOH) or a fractional-order hold (FROH).