Local stabilization for a hyperchaotic finance system via time-delayed feedback based on discrete-time observations

Abstract

This paper considers the local stabilization problem for a hyperchaotic finance system by using a time-delayed feedback controller based on discrete-time observations. The quadratic system theory is employed to represent the nonlinear finance system and a piecewise augmented discontinuous Lyapunov-Krasovskii functional is constructed to analyze the stability of the closed-loop system. By further incorporating some advanced integral inequalities, a stabilization criterion is proposed by means of the feasibility of a set of linear matrix inequalities under which the hyperchaotic finance system can be asymptotically stabilized for any initial condition satisfying certain constraint. As the by-product, a simplified criterion is also obtained for the case without time delay. Moreover, the optimization problems with respect to the domain of attraction are specially discussed, which are transformed into the minimization problems subject to linear matrix inequalities. Finally, numerical simulations are provided to illustrate the effectiveness of the derived results.