Constrained predictive synchronization of discrete-time chaotic Lur’e systems with time-varying delayed feedback control

• Published in: Nonlinear dynamics Vol. 72; no. 1-2; pp. 129 - 140
• Main Authors: Kwon, O. M., Son, J. W., Lee, S. M.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.04.2013; Springer Nature B.V
• Subjects: Automotive Engineering; Chaos theory; Classical Mechanics; Constraints; Control; Control systems; Delay; Discrete time systems; Dynamical Systems; Engineering; Feedback control; Linear matrix inequalities; Mathematical analysis; Matrix methods; Mechanical Engineering; Original Paper; Predictive control; Stabilization; Time synchronization; Vibration; Chaotic Lur’e systems; Delay-dependent criterion; Input constraint; Predictive synchronization
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-012-0697-3

This paper presents a predictive synchronization method for discrete-time chaotic Lur’e systems with input constraints by using time-varying delayed feedback control. Based on the model predictive control scheme, a delay-dependent stabilization criterion is derived for the synchronization of chaotic systems that is represented by Lur’e systems with input constraints. By constructing a suitable Lyapunov–Krasovskii functional and combining with a reciprocally convex combination technique, a delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality (LMI) formulation. The control inputs are obtained by solving a min-max problem subject to cost monotonicity, which is expressed in terms of LMIs. The effectiveness of the proposed method will be verified throughout a numerical example.