Robust Output Feedback Controller Design Based on Kalman Filter for Switched Positive Discrete-Time Systems

Abstract

In this paper, an interacting multiple model (IMM) Kalman filter is used to estimate non-measurable states in a linear switched positive discrete-time system (SPDS). The presence of process noise or measurement noise in a system is a common phenomenon. In positive systems, the problem of noise generally is ignored due to the possibility of eliminating the positive nature of the system. To solve the above problem, the powerful IMM-Kalman filter tool can be used along with the equilibrium point transfer in a targeted manner. Also, the effect of finite bounded disturbance is attenuated by the H∞ method. To guarantee the stability and positivity of the finite-time system with the asynchronous switching regime, a robust output feedback controller is designed. The original novelty of the method is designing a switched positive system in which the effect of disturbance and noise simultaneously have been reduced on it, and moving the equilibrium point of the system helps to improve efficiency and maintains its positivity. Then, the proposed method is implemented on the pest population dynamic as a stochastic model and compared by the root mean square error (RMSE) criterion with an existing output feedback method. The smallness of the RMSE criterion values for the three levels of disturbance in the presence of noise confirms the robustness and stability of the presented method