In this paper, we consider the local control problem for a chaotic finance system via the time-delayed feedback. Using the Lyapunov–Krasovskii stability theorem, the quadratic system theory, some integral inequalities, and rigorous mathematical analysis, we obtain a local stabilization condition by means of linear matrix inequalities. Then we discuss the estimate of the region of asymptotic stability and give the corresponding optimization problem. Also, we address the local control problem under the nondelayed feedback. Finally, we present numerical simulations to show the effectiveness of the proposed results.

中文翻译：

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混沌金融系统的时滞局部反馈控制

在本文中，我们通过延时反馈考虑了混沌金融系统的局部控制问题。使用Lyapunov–Krasovskii稳定性定理，二次系统理论，一些积分不等式和严格的数学分析，我们通过线性矩阵不等式获得了局部稳定条件。然后讨论渐近稳定区域的估计，并给出相应的优化问题。此外，我们在无延迟反馈下解决了本地控制问题。最后，我们提出数值模拟以显示所提出结果的有效性。