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

The problem of H1 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 H1 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 H1 controller according to actual events demonstrates the effectiveness of the method used in this paper. & 2015 Elsevier B.V. All rights reserved.