EE SEminar: A Generalization of Linear Positive Systems with Applications to Nonlinear Systems: Invariant Sets and the Poincare–Bendixon Property
(The talk will be given in English)
Speaker: Prof. Michael Margaliot
EE, Tel Aviv University
Monday, November 25th, 2019
15:00 - 16:00
Room 011, Kitot Bldg., Faculty of Engineering
A Generalization of Linear Positive Systems with Applications to Nonlinear Systems: Invariant Sets and the Poincare–Bendixon Property
Abstract
The dynamics of linear positive systems maps the positive orthant to itself. In other words, it maps a set of vectors with zero sign variations to itself. This raises the following question: what linear systems map the set of vectors with k sign variations to itself? We address this question using tools from the theory of cooperative dynamical systems and the theory of totally positive matrices. This yields a generalization of positive linear systems called kpositive linear systems, that reduces to positive systems for k = 1. We describe applications of this new type of systems to the analysis of nonlinear dynamical systems. In particular, we show that such systems admit certain explicit invariant sets, and for the case k = 2 establish the Poincare-Bendixon property for certain trajectories.
This is joint work with Eyal Weiss.
Short Bio
Michael Margaliot received the BSc (cum laude) and MSc degrees in Elec. Eng. from the Technion—Israel Institute of Technology in 1992 and 1995, respectively, and the PhD degree (summa cum laude) from Tel Aviv University in 1999. He was a post-doctoral fellow in the Dept. of Theoretical Math. at the Weizmann Institute of Science. In 2000, he joined the Dept. of Elec. Eng.–Systems, Tel Aviv University, where he is currently a Professor. His research interests include the stability analysis of differential inclusions and switched systems, optimal control theory, computation with words, Boolean control networks, contraction theory, and systems biology. He served as an Associate Editor for IEEE Transactions on Automatic Control during 2015–2017.