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\(H_\infty\) control of a chaotic finance system in the presence of external disturbance and input time-delay. (English) Zbl 1335.91123

Summary: This paper is concerned with the problem of \(H_\infty\) control for a class of chaotic finance systems with external disturbance. The purpose is to design a delayed state feedback controller such that the resulting error system is asymptotically stable with a prescribed \(H_\infty\) performance level. Using the Lyapunov functional method and Jensen inequality, delay-dependent sufficient criteria for the solvability of this problem are established in terms of linear matrix inequality (LMI). Moreover, numerical simulations are provided to demonstrate the effectiveness of the proposed theoretical results.

MSC:

91G80 Financial applications of other theories
37N40 Dynamical systems in optimization and economics
93B36 \(H^\infty\)-control
93C95 Application models in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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