Sliding Mode Control for Uncertain T-S Fuzzy Singular Biological Economic System

Abstract

In this paper, the design of sliding mode controller for a singular biological economic model with a stage structure and uncertain parameters is studied. First, a biological economic system with uncertain parameters for the invasion of alien species is modeled by a singular system. Then, according to the theory of the T-S fuzzy system, an uncertain T-S fuzzy singular model is established and the stability of the model at the positive equilibria is discussed. Furthermore, a fuzzy integral sliding surface and a sliding mode controller are designed for the T-S fuzzy singular system with an uncertain term. At the same time, the state trajectories can be driven onto the integral sliding surface in finite time and a sufficient condition about the global asymptotic stability of sliding motion is obtained. Finally, a simulation is given to verify the effectiveness of the obtained results.