Zeros of sampled systems with fractional order hold implemented by zero order hold

For a sampled control system, replacing zero order hold with fractional order hold has been shown to improve the stability of zeros of the system. However, it is difficult to use the fractional order hold in practice. In this study, an approximated method of using fractional order hold is proposed. The theorem for stability of zeros of the sampled system is proved as the sampling period is small. It is shown that the approximated fractional order hold has the same advantages as the accurate one. The results could be useful in the design of a digital control system.