Stability analysis via contraposition Nyquist approach for sampled-data systems with auxiliary continuous-time feedback

In this report, firstly, the lifted models of sampled-data systems formed by connecting a generalized linear continuous-time, time-invariant subsystem (the control plant) is introduced. Then, an auxiliary continuous-time feedback is therefore attached. It is built with a linear discrete-time, time-invariant subsystem (the feedback controller) via a periodic sampler along with a holding apparatus. The feedback is operated by means of the time-domain lifting technique. By exploiting the complex-domain characteristics of the lifted models, an internal stability analysis is contrived under a generalized Nyquist criterion in such sampled-data systems. The analysis is constructed by examining the contraposition return difference relationships between the open- and closed-loop characteristic polynomials. We would like to mention that the suggested necessary and sufficient stability conditions entail no open-loop poles distribution information, and are simply independent of the encirclement number and orientation of the Nyquist loci. Thus, the generalized Nyquist criterion presents us with purely graphical stability conditions.