$H_{\infty}$ Synchronization of Networked Master–Slave Oscillators With Delayed Position Data: The Positive Effects of Network-Induced Delays

This paper is concerned with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synchronization of coupled oscillators in a master-slave framework, in which the oscillators cannot be stabilized by nondelayed sampled position data, but can be stabilized by sampled position data with delays restricted by nonzero lower bounds and upper bounds. A configuration of networked master-slave oscillators with a remote controller is first constructed. Then the positive effects of delays on master-slave synchronization are investigated. Some delay-dependent H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> synchronization criteria are derived by constructing augmented discretized Lyapunov-Krasovskii functionals for determinate sampling and stochastic sampling, respectively. The controller can be designed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to verify the theoretical results. It is shown that the maximum allowable sampling period in the case of stochastic sampling is larger than the one in the case of determinate sampling. Stochastic sampling can also provide a tradeoff between network-induced delays and the sampling periods, enhancing the master-slave synchronization performance.