Properties of Zeros of Sampled Systems

Abstract

Poles and zeros play an important role in control system design. This paper clarifies the properties of zeros of a single input-single output discretized system composed of a sampler and a zero-order hold. It is shown that the property that the number of real zeros between any two real poles is even or odd is preserved for the discretized system with any sampling period which assures all the poles of the continuous controlled object lie in the primary strip of s-plane. This property is also true for a sampled system considering any computational time delay and the sampled system has at least an unstable limiting zero for small sampling periods. Sufficient conditions, which guarantee the sampled system has only stable zeros or an unstable zero regardless of the sampling period, are presented using the derived properties.