Linear programming based dynamic output-feedback controller for positive systems

This paper addresses an improved approach to dynamic output-feedback control design of positive systems. By using a simple matrix transformation technique that a matrix can be described via the sum of all its column vectors, a linear programming based controller design approach for nominal positive systems is proposed. Subsequently, the proposed approach is extended to interval positive systems. The present approach contains three merits that are different from existing ones: (i) it employs the linear programming technique while existing ones adopt the linear matrix inequalities technique; (ii) it provides a more general controller without negative restriction while existing ones may require the negativity of the controller gain matrix; (iii) it is easy to be extended to other issues of positive systems while this may not always be possible for existing approaches. Finally, a numerical example is provided to verify the effectiveness of the proposed design.