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This paper deals with a pest control strategy integrated the disease, enemies, pesticides and competition factors, which is described by an impulsive dynamical system with static state feedback controller. It extends the finite-time stability to the problem designing a double control strategy. Compared with the ordinary differential system, the unstable coexistence equilibrium can be stabilized by impulsive control. Furthermore, the infinite time stability step by step of finite-time stable control through numerical simulations can be obtained. The results imply that the double control is a more effective and environmentally sensitive strategy than the unique impulsive control. That is, the few times spraying chemical pesticides under the double control which we only need.
How to Cite this Article:
Xiaoxi Yu, Yongzhen Pei, Yunfei Lv, Xiyin Liang, Infinite and finite-time stability of an impulsive dynamical system with feedback control, Journal of Nonlinear Functional Analysis 2015 (2015), Article ID 13.