Abstract
In this article, we evaluate how the random environmental fluctuations affect the interplay between the sugarcane borer (Diatraea saccharalis) and its egg parasitoid (Trichogramma galloi). In order to procure an optimal control input, we considered the uncertainties in the control agent that leads to a non‐fragile control synthesis. Due to the existence of a stochastic environment and uncertainties in the control agent, the impulsive biological control is introduced to stabilize the situation. By means of the classical Lyapunov method, a new sufficient condition for exponential stability of our proposed population model through non‐fragile control and impulsive biological control is established. With the assistance of linear matrix inequality (LMI) solvers, non‐fragile controllers can be obtained effortlessly. In addition, we provide simulation studies that are primarily based on the sugarcane borer system to demonstrate the effectiveness and benefits of our proposed model.