Distributed control using positive quadratic programming

State space descriptions with nonnegative coefficients define an important class of dynamical systems, so-called positive systems, with many applications in science and technology. In particular, they appear naturally in the study of electrical power systems. Positive systems have properties that are particularly attractive for distributed control. For example, they allow stability to be verified without conservatism in a distributed way. Moreover, optimal controllers with constraints can be designed using Positive Quadratic Programming. This is a special case of standard quadratic programming, which exploits positivity of coefficients in objective function and constraints. The technique is here illustrated by examples from electrical networks.