Zero dynamics of sampled-data models for nonlinear multivariable systems in fractional-order hold case

The paper is concerned with the properties of approximate sampled-data models and their zero dynamics, as the sampling period tends to zero, composed of a fractional order hold (FROH), a continuous-time multivariable plant and a sampler in cascade. The emphasis of this paper is the stability of discrete zero dynamics with the generalized gain ββ of the FROH, where we also present a condition to assure the stability of the sampling zero dynamics, which they have no counterpart in the underlying continuous-time system, of the resulting model. Similar to the linear case, the parameter ββ is the only factor in affecting the stability of discrete zero dynamics, and the appropriate ββ is determined to obtain the FROH that provides zero dynamics as stable as possible, or with improved stability properties even when unstable, for a given continuous-time multivariable plant. The study is also shown that the stability of the sampling zero dynamics is improved compared with a zero-order hold (ZOH).