Parameter-Dependent Positive Observers for LPV Positive Systems

In this research, we suggest how to design parameter-dependent positive observers (PDPOs) and PDPO-based controllers (PDPOBCs) for linear parameter-varying (LPV) positive linear systems in the continuous-time domain. The physical meaning of the positive observer differs from the general observer. In fact, the main opinion of the positive observer is to guarantee that all the estimates and also, the estimation error never become negative at any time. Unlike previous positive observers, this article focuses on them for the LPV positive system through four theorems. Based on the polytopic frame, the proposed PDPO estimates the state variables of positive LPV systems exactly and in terms of linear matrix inequality (LMI). Consequently, it guarantees the closed-loop system’s stability and positivity. To verify the feasibility and applicability of the proposed theorems, simulation-based results of each theorem are provided for numerical plants, and also for real medical plant (the Thyroid hormone metabolism’ system). Compared with some previous methods for positive observers, the proposed observation is with minimum error and it is faster and tighter.