Improvement of stability of zeros in discrete-time multivariable systems using fractional-order hold

This paper is concerned with the stability of zeros of the discrete-time multivariable systems composed of a fractional-order hold (FROH), a continuous -time plant and a sampler in cascade. The properties of the limiting zeros are studied and a condition for obtaining stable zeros for sufficiently small sampling periods is derived. An approximate fractional-order hold (AFROH) is proposed as an implementation of FROH. It is shown that the AFROH as well as the FROH can locate the zeros of discrete-time multivariable systems inside the stable region and improve stability properties when the zero-order hold (ZOH) cannot. Experimental results of adaptive control with AFROH demonstrate a significant improvement of control performance compared with the use of a ZOH.