Minimum-phase criteria for sampled systems via symbolic approach

In this paper, we propose a symbolic approach to determine the sampling-time range which guarantees minimum-phase behaviours for a sampled system with a zero-order hold. By using Maple, a symbolic manipulation package, the symbolic transfer function of the sampled system, which contains sampling time T as an independent variable, can be easily obtained. We then adopt the critical stability constraints to determine the sampling-time range which ensures that the sampled system has only stable zeros. In comparison with existing methods, the proposed approach in this note has less restrictions on the continuous plant and is very easy to implement in any symbolic manipulation package. Several examples are illustrated to show the effectiveness of this approach.