A unified Lyapunov-like characterization for predefined time synchronization of nonlinear systems

• Published in: Nonlinear dynamics Vol. 112; no. 11; pp. 8775 - 8787
• Main Authors: Zhang, Mengjiao, Zang, Hongyan, Shi, Zhudong
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2024; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Control; Control algorithms; Control systems design; Controllers; Design; Dynamic stability; Dynamical Systems; Engineering; Mechanical Engineering; Nonlinear systems; Review; Robust control; Sliding mode control; Time synchronization; Vibration; Lyapunov-like characterization; Predefined time stability; Stability of nonlinear systems; Sliding mode control; Chaos synchronization and control
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-024-09506-x

In this paper, we present a new design for predefined time stable Lyapunov-like characterizations. Our approach combines several previously proposed Lyapunov characterizations and provides a unified idea for designing predefined time stable dynamic systems, based on which the framework of the predefined time sliding mode controller (PTSMC) is designed. First, we define Class - Z functions and use them to design a unified form of Lyapunov-like characterization; moreover, we prove that it satisfies the predefined time stability by using the comparison principle. Second, a class of predefined time stable dynamic systems is developed based on this constructed function, and its predefined time stability properties are confirmed by Lyapunov theory. Finally, the dynamic system is used to construct a sliding mode controller, and a universal framework for PTSMCs is designed. By applying the above to chaos synchronization, numerical simulations demonstrate the universality and the feasibility of this unified control framework.