H∞ control of T-S fuzzy fish population logistic model with the invasion of alien species

The problem of H∞ control for a fish population logistic model with the invasion of alien species is studied via a T-S fuzzy control approach in this paper. Firstly, the harvested capability induced by economic factors and purification capability induced by invasion of alien species are analyzed. Secondly, the corresponding bio-economic model is established by taking the above two factors into account. Thirdly, the singularity-induced bifurcation (SIB) and impulsive behavior of the resultant bio-economic model are investigated. After that, a T-S fuzzy system is used to describe the nonlinear system for the bio-economic model with added input disturbance. A sufficient condition is proposed to satisfy H∞ norm of the system by using the Lyapunov theory and a linear matrix inequality approach. Finally, a modified differential transform method is exploited to present the invasion system to analyze the characters. The application of H∞ controller according to actual events demonstrates the effectiveness of the method used in this paper.