Robust Stability and Stabilization of 2D Positive System Employing Saturation

This work is concerned with the issue of stability analysis and controller synthesis for a class of Fornasini–Marchesini second-type systems with polytopic uncertainty, state delays and saturation nonlinearity. Firstly, by utilizing the co-positive Lyapunov function method, sufficient conditions in the linear programming setting are presented assuring the positivity and robust asymptotic stability of the proposed systems. Then, both the state feedback controller and the observer-based state feedback controller are considered based on the obtained results. In addition, the design schemes of the related controller gain matrices are also explicitly provided. Finally, two illustrative examples are given to demonstrate the effectiveness of the method outlined in this paper.