Observer-Based Stabilization of Positive Linear System With Disturbances

Abstract

This article addresses the disturbance rejection and output stabilization control of positive linear systems. First, two disturbance observers (DOs) are proposed to estimate actuator-channel and sensor-channel disturbances, while a positive state observer is designed for state estimation. Subsequently, a state observer-based controller is constructed, integrated with a static output feedback controller and the outputs of the two DOs, to form a composite controller. Without relying on the full-state measurement, this design ensures that disturbances are compensated, and the positivity and stability of the closed-loop system are guaranteed. Finally, a linear programming-based iterative optimization algorithm is developed to compute feasible gains for the controller and observers, and its effectiveness is verified through two numerical simulations.