A Limiting Property of the Inverse of Sampled-data Systems on a Finite Time Interval

The Case of Relative Degree 2

Abstract

It is tricky to predict the limiting property of the inverse of sampled-data systems obtained from linear continuous-time systems in a finite-time domain when the sampling period goes to 0. The reason is that, in some cases, all zeros tend to the boundary between the stable and unstable areas when the sampling period goes to 0, while the number of sample points goes to infinity. In this paper, we discuss the limiting property of the case of relative degree 2. It is demonstrated that inverse sampled-data systems converge to inverse continuous-time systems on the finite-time domain independently of the stability of zeros.