<p>Bemisia tabaci is an agricultural pest with great impact, widely distributed in more than 90 countries and regions. In order to slow down the spread of Bemisia tabacti, Neoseiulus barkeri is selected as a natural enemy, and a generalized Holling-III functional response pest-natural enemy model with additional food supply for Neoseiulus barkeri is proposed. The dynamical behavior of the model is investigated, including the existence and boundedness of the solution and the existence and stability of the equilibrium points. In order to effectively control the spread of Bemisia tabacti, in addition to relying on the inhibition of natural enemies, human control is also necessary. In this paper, two pest management models with threshold control are developed: the Filippov control model and the state feedback control model. For the Filippov control model, sliding mode dynamics together with the existence of pseudo-equilibrium are studied. For the state feedback control model, the existence of periodic solutions are discussed by constructing a Poincaré map, and their stability are verified by Analogy of Poincaré criterion. Finally, numerical simulations in MATLAB are carried out to illustrate the main results presented in the work. This study provides some reference for the integrated control of Bemisia tabaci.</p>