Improving the stability properties of sampling zeros of multivariable discrete model via Taylor method and multirate fast sampling

It is well known that multirate input and hold, such as a generalized sample hold function (GSHF), can be used to shift the sampling zeros of a discrete-time model for a continuous-time system. This paper deals with the stability of sampling zeros, as the sampling period tends to zero, of discrete-time models that are composed of a GSHF, a continuous-time multivariable plant and a sampler in cascade. We propose a hold design that places the sampling zeros asymptotically to the stable region by deriving the approximate expressions of the sampling zeros as power series expansions with respect to a sampling period. The focus is on the evolution of the complex plant for the sampling zeros with the design parameters αj of the GSHF. These parameters are only determined to propose the GSHF that obtains sampling zeros as stable as possible, or with improved stability properties even when unstable, for a given continuous-time multivariable system. The research is extended by obtaining the optimum value of αj for sufficiently small sampling periods and a continuous-time plant, and meanwhile a new stability condition of the sampling zeros is obvious weaker than that of ZOH or FROH case. Key–Words: Stability properties, sampled-data multivariable models, sampling zeros, generalized sample hold function, fast sampling, Taylor series expansions.