Argument-Principle-Based Criteria for Structural Features in Non-Essentially-Real Systems

Recently, an argument-principle-based criterion for controllability/observability in a class of essentially-real dynamical systems is suggested and rigourously proved in [18] by the same authors. In this paper, we try to generalize the idea to non-essentially-real systems that possess complex eigenvalues in the state matrices. Firstly, this paper establishes an argument-principle-based technique for coprime testing among real polynomials. Secondly, by exploiting the same technique, the paper develops a frequency-domain framework for structural features in terms of controllability/observability in linear dynamical systems. More precisely, different from the PBH (Popov-Belevitch-Hautus) and Gramian criteria, which provide matrix-rank and matrix-exponential-integral conditions from a geometric and algebraic viewpoint, the suggested criteria present Nyquist-like testing conditions, regarding controllability and observability.