Sampled-data model for nonlinear coupled Van der Pol oscillators

For sampled-data controller design of nonlinear continuous-time systems, it is important to derive a good approximate sampled-data model because the exact sampled-data model for nonlinear systems is often unavailable to the controller designers. In the multi-input multi-output (MIMO) case, the authors have proposed an accurate approximate model which includes extra zero dynamics corresponding to the relative degree of the continuous-time nonlinear system. Such extra zero dynamics are called sampling zero dynamics. A more accurate sampled-data model is, however, required when the relative degrees of a continuous-time nonlinear plant are two. The reason is that the closed-loop system becomes unstable when the more accurate sampled-data model has unstable sampling zero dynamics. This paper derives the sampling zero dynamics of the more accurate sampled-data model for coupled Van der Pol oscillators and analyzes the relationship between the stability of the closed-loop system and the stability of the sampling zero dynamics of a proposed model.