Mathematics – Optimization and Control
Scientific paper
2010-10-18
Mathematics
Optimization and Control
Scientific paper
We here extend the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. We then exploit this result to provide an easy construction procedure of all (not necessarily minimal) state space realizations of generalized positive functions. As a by-product, we partition all state space realizations into subsets: Each is identified with a set of matrices satisfying the same Lyapunov inclusion and thus form a convex invertible cone, cic in short. Moreover, this approach enables us to characterize systems which may be brought to be generalized positive through static output feedback. The formulation through Lyapunov inclusions suggests the introduction of an equivalence class of rational functions of various dimensions associated with the same system matrix.
Alpay Daniel
Lewkowicz Izchak
No associations
LandOfFree
The positive real lemma and construction of all realizations of generalized positive rational functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The positive real lemma and construction of all realizations of generalized positive rational functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The positive real lemma and construction of all realizations of generalized positive rational functions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-305779