Master-slave synchronization of Lur’e systems with sector and slope restricted nonlinearities. (English) Zbl 1228.34076
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:
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34H10 | Chaos control for problems involving ordinary differential equations |
| 93B52 | Feedback control |
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