Seminar Details
2016-05-20 (15:00) : Differentially positive systems: asymptotic behavior and converse results
At Euler building (A002)
Organized by Mathematical Engineering
Speaker :
Fulvio Forni (University of Cambridge (UK))
Abstract :
Differential analysis aims at inferring global properties of nonlinear behaviors from the local analysis of the linearized dynamics. The novel notion of differential positivity extends linear positivity to the nonlinear setting: a nonlinear system is differentially positive if its linearization along trajectories leaves a cone (field) invariant. Notably monotone systems are differentially positive. Differential positivity extends monotonicity to manifolds, replacing order relations with local orders. The property strongly restricts the asymptotic nonlinear behavior, through suitable extensions of Perron-Frobenius theory and of results on contraction of the Hilbert metric. Motivated by the importance of positivity in linear systems theory, we discuss both the relevance of the property for applications and how much the property restricts the behavior of a nonlinear system.