On Existence of Uniformly Marginally Stable Zeros of Linear Sampled-Data Systems and Its Application to Stable Inversion-Based Control

This paper investigates a class of sampled-data control systems in which at least one of the discrete-time zeros remains on the unit circle regardless of the sampling period. This type of zero is referred to as an “uniformly marginally stable” (UMS) zero. Utilizing this novel concept, we present necessary conditions as well as sufficient conditions for the continuous-time plant whose sampled-data model has an UMS zero. The theoretical finding of this paper newly highlights the significance of the symmetry regarding the zeros and poles of the continuous-time plant, as it plays a vital role in enforcing a discrete-time zero of the sampled-data system to be UMS, for both discretization zeros and intrinsic zeros. We develop the theory for sampled-data systems employing a conventional sampler and a zero-order hold together with a single-input single-output continuous-time plant, and then observe that certain results can be extended to the generalized holds. As an application, we construct a discrete-time stable inversion-based control in the sampled-data setting and establish a condition for continuous-time plants that allow for this type of control, in which absence of such an UMS zero is crucial.