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This paper deals with the stability characteristics of zeros for sampled-data models with a class of triangle sample and hold realized by a traditional zero-order hold. For any controlled models in the modern industrial system, using a digital control strategy has been shown to provide the means to achieve the assigned objectives. In this process, one must utilize the sample and hold device to obtain the sampled-data models. Previous studies have shown that the triangle sample and hold can improve the stability properties of zeros of a sampled-data control system compared with zero-order hold. However, it is difficult to use triangle sample and hold in practice. In this paper, an approximated method of using triangle sample and hold is proposed. More importantly, on the basis of that method, we explicitly derive the corresponding accurate sampled-data model of controlled models. In addition, we also provide the expression for sampling zeros and the theorem for the stability of a linear control system in the fast sampling process. The results of this paper show that the proposed method has the same advantages as the accurate one. Finally, theoretical findings are validated through numerical simulations with different considerations.

Zero dynamics have crucial effect on system analysis and controller design. In the control analysis process, system performance is influenced by the unstable zero dynamics, greatly. This study concerns with the properties of limiting zero dynamics when the signal of controlled continuous-time systems was reconstructed by forward triangle sample-and-hold (FTSH). FTSH is a newly sample and hold method in the signal reconstruction area. However, more theoretical details about the limiting zero dynamics of the resulting discrete-time systems need to be revealed. Firstly, the framework for the limiting zero dynamics in the situation of sufficiently small or large sample period is introduced. Furthermore, this study provides the stable conditions of limiting zeros in the two different sampling situations. The results indicate that one can select a suitable variable parameter value of FTSH to replace the sampling zeros of discrete-time system locate inside the stable region. This paper also reveals the truth that FTSH has the outstanding advantage compared with the BTSH using theoretical analysis method. Finally, example simulations verify the effectiveness of the results in this study.