H∞ control for a hyperchaotic finance system with external disturbance based on the quadratic system theory

This paper considers the $ H_\infty $ control problem for a hyperchaotic system with energy-bounded disturbance under the delayed feedback controller. Using the quadratic system theory, an augmented Lyapunov functional, some integral inequalities and rigorous mathematical derivations, a sufficient condition is first established by using linear matrix inequalities under which the closed-loop system can achieve some desirable performances including the boundedness, the $ H_\infty $ performance and the asymptotic stability. Subsequently, several convex optimization problems are formulated to obtain the optimal performance indices. Finally, numerical simulations are presented to illustrate the effectiveness of the obtained results.