Observer-based sliding mode controller design for singular bio-economic system with stochastic disturbance

In this paper, we investigate the problems of sliding mode observer design and observer-based integral sliding mode control for a class of singular bio-economic systems with stochastic disturbance. Initially, we establish a bio-economic system with the alien invasive species and stochastic disturbance. Then, a new integral sliding surface is constructed based on the multiplication of sliding variables and negative definite matrix for the error system. The advantage of this method is that it not only stabilizes the sliding variables, but also eliminates the restrictive assumptions often used in sliding mode control of the singular bio-economic systems with stochastic disturbance. Finally, an augmented system is constructed and the linear matrix inequality technique is used to determine the admissibility of the mean square exponent. Furthermore, an observer-based sliding mode controller is designed so that the reachability conditions can be guaranteed. The validity of the results is verified by a numerical simulation.