A sufficient and necessary condition for stabilization of zeros in discrete-time multirate sampled systems

Abstract

It is well known that the presence of unstable zeros limits the control performance, which can be achieved, and some control schemes cannot be directly applied. This manuscript investigates a sufficient condition for stabilization of zeros in the discrete-time multirate sampled systems. It is shown that the discretization zeros, especially sampling zeros, can be arbitrarily placed inside the unit circle in the case of relative degree being greater than or equal to three and multirate input and hold, such as generalized sampled-data hold function (GSHF), for the linear continuous-time systems when the sampling period T tends to zero. Moreover, the authors further consider the multivariable case, which has a similar asymptotic behavior. Finally, the simulation proves the validity of the method, and we also propose a hold design that places the sampling zeros asymptotically to the origin for fast sampling rates.