Examining Bounded Realness with Generalized Nyquist Loci in Multivariable Feedback Configurations

In this paper, we propose an alternative frequency-domain interpretation about bounded realness and H-infinity norm evaluation in the linear time-invariant (or simply LTI) multivariable continuous-time feedback configuration setting. The technique can be implemented numerically as well as geometrically by means of a class of generalized Nyquist loci without open-loop unstable pole distribution, locus orientation prespecification and unstable-pole-related encirclement counting. Different from the bounded real lemma and the Hamiltonian test that are essentially matrix algebraic approaches, the results here spot some new light on bounded realness in a complex functional and geometrical fashion. The generalized Nyquist approach is furthermore exploited carefully for the H-infinity norm estimation in form of geometric bisection algorithms. Numerical examples are included to illustrate the main results.