Positive Filtering of Positive Complex Networks Using Linear Programming

This paper investigates the filtering design of positive complex networks in both discrete- and continuous-time contexts. A positive filtering is proposed for discrete-time complex networks. The filtering gain matrices are designed based on a matrix decomposition approach. All positivity and stability conditions are described in terms of linear programming. A novel positivity analysis framework is constructed for complex networks and the corresponding error systems and a gain filtering design is solved using copositive Lyapunov function. The presented filtering design approach is developed for continuous-time complex networks. Finally, an example is provided to verify the validity of the proposed filtering.