An improved approach to controller design of positive systems using controller gain decomposition

This paper aims to propose an improved controller design approach for positive systems in both continuous-time and discrete-time contexts. First, by decomposing the controller gain matrix into components, compact conditions that is simple and easy to be computed for guaranteeing the positivity and stability of positive systems is formulated. Based on the obtained conditions, new stabilization results and subsequent controller design are formulated with improvements in both the feasibility of conditions and the generality of the controller. All conditions are solvable in terms of linear programming. Compared with existing approaches in the literature, the new design approach constructs a controller with simpler forms and less restrictions. Meanwhile, the efficiency and advantage of the present approach are verified by application to the typically studied problems in the literature. Some discussions on the proposed approach are provided to show its potential applications on positive systems. Finally, three comparison examples are given to verify the merits of the theoretical findings.