Tuesday 28 Jun 2016: Dynamics seminar: Stability and Control of Positive Dynamical Systems
Prof. Stuart Townley - University of Exeter
Positive dynamical systems arise in numerous applications where dependent variables are necessarily non-negative. These applications range from biology, chemistry and ecology, to genetics and medicine, through to economics and engineering. For linear systems, the theory of positive systems is rooted in the seminal work of Perron-Frobenius. For nonlinear positive systems there is a deep and profound stability analysis found in the works of Hirsch, Smith, Ranft and Krause. The control of positive systems has attracted much interest including the classical results of Rinaldi and Farina, and more recent work of Briat, Rantzer and others. In this talk, I will present recent results on a trichotomy of stability for positive systems and also lay out some ideas for a new "positive state control theory", especially focusing on adaptive feedback control of positive systems, and applications to pest management.