In my opinion there a'nt a analytical relation of an SVD plot and induction of poles and zeros from it. However there is relation between SVD and the eigen values of matrix. if this matrix is corespending to the evolution matrix A of a state representation then we can calculate the poles of this system from the SVD.
Hmm, why 'answer' got lost ... do you have a H(s) model to work with? If so, try (free) FC-Compiler (https://www.researchgate.net/project/FC-Compiler-the-FortranCalculus-Compiler-Alpha-version-2 ). There is an app that may help ... Match-n-Freq (http://fortrancalculus.info/apps/match-n-freq.html ) that does find pole/zero(s). See attached document for H(s) write-up and plots.