Asymptotic Properties of Sampling Zero Dynamics for Nonlinear Systems in the Case of Time Delay and Relative Degree Two

It is well-known that stability of zero dynamics is often inevitable to the controller design. And most real world plants often involve a time delay. This paper investigates the zero dynamics, as the sampling period tends to zero, of a sampled-data model composed of a zero-order hold (ZOH), a continuous-time plant with a time delay and a sampler in cascade. We first present how an approximate sampled-data model can be obtained for the nonlinear system with relative degree two, and the local truncation error between the output of obtained model and the true system output is of order , where T is the sampling period and r is the relative degree. Furthermore, we also propose the additional zero dynamics in the sampling process, which are called the sampling zero dynamics, and the condition for assuring the stability of sampling zero dynamics for the desired model is derived. The results presented here generalize a well-known notion of sampling zero dynamics from the linear case to nonlinear systems.