Stabilisation of positive systems with generalised disturbances

Abstract

Robustness of positive systems with respect to disturbances is a challenging issue of both theoretical and practical importance. In this study, the stabilisation control problem of positive systems with disturbances is investigated. More generalised disturbances are considered here, including positive modelled disturbances and general disturbances. A disturbance observer is designed to estimate the disturbances and a sufficient and necessary condition for stabilisation is derived. For positive disturbances, a sufficient condition with the use of the convergence law for the existence of controller is proposed, and this problem can be formulated as a linear programming problem. Furthermore, the corresponding theory is expanded to generally modelled disturbances, which enriches the theories about anti-disturbance control of positive systems. Meanwhile, the analysis is given in detail to promote the theoretical completeness, including conservations of hypothesis and positivity constraints of disturbance estimation values. Simulation results show that the proposed scheme can guarantee the positivity of systems and improve the system performances for generalised disturbances.