Plenary Lecture

Positive Linear Systems with Delays

Professor Tadeusz Kaczorek
Warsaw University of Technology
Poland

Abstract: In positive systems inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear systems behavior can be found in engineering, management science, economics, social sciences, biology and medicine, etc.

Positive linear systems are defined on cones and not on linear spaces. Therefore, the theory of positive systems is more complicated and less advanced.

In the plenary lecture necessary and sufficient conditions for the positivity, reachability and controllability of positive 2D systems will be established. The realization problem for positive discrete-time and continuous-time linear systems will be formulated and solved. Procedures for computation of positive realizations for a given transfer matrix will be proposed. The considerations will be illustrated by numerical examples and by some applications. New class of positive hybrid systems and positive Lyapunov systems will be addressed.