s-domain generalized Nyquist criteria for double-loop sampled-data systems

In this paper, we develop an alternative frequency-domain stability analysis technique for sampled-data systems with auxiliary continuous-time controllers, in addition to the discrete-time ones, which form a class of double-loop feedback configurations, by working directly on their s-domain return difference relationships. This method is independent of the lifted models and employs merely the s-domain expressions and relationships of all the system components and signals involved. The suggested stability conditions are stated in a Nyquist-like fashion, which involve neither open-loop unstable poles distribution, nor specific locus encirclement counting and orientations of the generalized Nyquist loci.