Stability analysis of discrete-time positive polynomial-fuzzy-model-based control systems through fuzzy co-positive Lyapunov function with bounded control

摘要

This study employs a novel fuzzy co-positive Lyapunov function to investigate the stability of discrete-time polynomial-fuzzy-model-based control systems under positivity constraint. The fuzzy co-positive Lyapunov function consists of a number of local sub-Lyapunov function candidates which includes the positivity property of a non-linear system and the contribution of each sub-Lyapunov function candidates depends on the corresponding membership functions. Imperfect premise matching design concept is used for the design of a closed-loop polynomial fuzzy controller based on the constructed polynomial fuzzy model. The bounded control signal conditions (upper and lower boundary demands on control signal) are included in the Lyapunov stability and positivity conditions, in which all are formulated in the form of sum-of-squares conditions. A numerical example is given to validate the proposed approach.