Linear Programming Based Decentralized Control for a Class of Interconnected Positive Systems

In this paper, the problems of positivity and exponential stability analysis as well as decentralized control design are addressed for a class of interconnected positive systems(IPSs), which is composed of a family of positive subsystems and an interconnected function term. Firstly, a sufficient and necessary condition of positivity is provided for the considered IPSs. Then, a sufficient condition of exponential stability is derived for the IPSs based on a linear copositive Lyapunov function method. Further, an effective decentralized controller design scheme with the conditions formulating in the linear programming(LP) form is proposed to solve the control design problem for the IPSs. Finally, the effectiveness of the designed LP-based decentralized controller scheme is illustrated by an example.