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Zbl 1228.34076
Ji, D.H.; Park, Ju H.; Won, S.C.
Master-slave synchronization of Lur'e systems with sector and slope restricted nonlinearities. (English)
[J] Phys. Lett., A 373, No. 11, 1044-1050 (2009). ISSN 0375-9601

Summary: This letter presents a synchronization method for Lur'e systems with sector and slope restricted nonlinearities. A static error feedback controller based on the Lyapunov stability theory is proposed for asymptotic synchronization. The Lyapunov function candidate is chosen as a quadratic form of the error states and nonlinear functions of the systems. The nonlinearities are expressed as convex combinations of sector and slope bounds by using convex properties of the nonlinear function so that equality constraints are converted into inequality constraints. Then, the feedback gain matrix is derived through a linear matrix inequality (LMI) formulation. Finally, a numerical example shows the effectiveness of the proposed method.

MSC 2000:: *34D06
34D08 Lyapunov exponents
34A34 Nonlinear ODE and systems, general
34H10
93B52 Feedback control

Keywords: synchronization; Lur'e systems; sector and slope restricted nonlinearity; LMI

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