The stability analysis and control of uncertain singular biological economic system with invasion of alien species based on sliding mode control

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Abstract
In this paper, we analyse the robust stability and control problem of singular biological economic systems with uncertain items based on sliding mode control. Firstly, we establish a biological economic systems with uncertain parameters for the invasion of alien species. We get the uncertain T-S fuzzy singular systems by using a set of fuzzy rules and analyse the robust stability of nonautonomous uncertain T-S fuzzy singular systems. Then, we design the fuzzy integral sliding surface and controller. We prove that the state trajectories can arrive integral sliding surface in finite time, and we also provide the sufficient conditions that the sliding motion is globally asymptotically stable. Lastly, we give practical example to show the effectiveness and correctness of our conclusions about Scavenger invasion to Zhanjiang Chikan reservoirs. By using the real data and Fourier series to approximate the uncertain parameters, we verify the effectiveness and correctness of the sliding mode control.

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