2010/10/18 by Daniel Alpay, Alpay, Daniel, Izchak Lewkowicz +1
Engineering · #15A45 #15B48 #26C15 #47L07 #93B15 #93B52 #93D10 #94C05 #Advanced Control Systems Optimization #Complex Variables (math.CV) #Control Systems and Identification #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1010.3548
openalex publication_date 2010/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We here extend the well known Positive Real Lemma (also known as the\nKalman-Yakubovich-Popov Lemma) to complex matrix-valued generalized positive\nrational function, when non-minimal realizations are considered. We then\nexploit this result to provide an easy construction procedure of all (not\nnecessarily minimal) state space realizations of generalized positive\nfunctions. As a by-product, we partition all state space realizations into\nsubsets: Each is identified with a set of matrices satisfying the same Lyapunov\ninclusion and thus form a convex invertible cone, cic in short. Moreover, this\napproach enables us to characterize systems which may be brought to be\ngeneralized positive through static output feedback. The formulation through\nLyapunov inclusions suggests the introduction of an equivalence class of\nrational functions of various dimensions associated with the same system\nmatrix.\n