有限時間区間におけるサンプル値系の極限零点と逆システムの性質について

抄録

If a linear continuous-time system is considered on a finite time domain, there is no diverging variable of the inverse systems even if the transfer functions have unstable zeros. However, if a sampled-data systems is discussed on the finite time domain, it is not a trivial matter to determine whether there is diverging variables or not because shrinking the sampling period on the finite time interval implies increasing the number of sampling points. There is a possibility that the increase of the time interval for the discrete-time system may cause diversion. In this paper, we show that there is no diverging variable of the inverse of sampled-data systems with 0-order holders if the relative degree of the continuous-time transfer function is 0 or 1. It is also demonstrated that such a property is independent of stability of zeros. The main result implies that we can formulate a problem of digital iterative learning control as a minimization problem of output errors on the sampling points.