Novel LKF Method on<i>H<sub>∞</sub></i>Synchronization of Switched Time-Delay Systems
Qihan Qi, Xinsong Yang, Zhilu Xu, Meijie Zhang, Tingwen Huang
Abstract
This article investigates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> global asymptotic synchronization (GAS) of switched nonlinear systems with delay. By introducing mode-dependent double event-triggering mechanisms (DETMs), the communication resources in both system–controller (S-C) channel and controller–actuator (C-A) channel are saved as much as possible. By designing a new multiple Lyapunov–Krasovskii functional (LKF) with time-varying matrices and developing novel analysis techniques such that the increment of the LKF at switching instant is smaller than one, not only the conservatism of obtained results is greatly reduced but also the nonweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula> -gain is convenient to be derived without using any conservative transformation. The exclusion of the Zeno behavior of the DETMs is proved. Synchronization criteria formulated by linear matrix inequalities (LMIs) are given, by which the control gains, event-triggering weights, as well as the minimum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula> -gain are simultaneously designed. Numerical examples demonstrate the low conservatism of the theoretical analysis. Meanwhile, image processing on the basis of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> GAS is provided to further illustrate the perfect performance.