Synchronization for stochastic switched networks via delay feedback control

Abstract

In this paper, asymptotical synchronization in mean square, $H_\infty$-synchronization, and almost sure exponential synchronization are developed for a class of stochastic switched networks with Markov switching and Brown noise using a delay feedback controller that depends on the past state. By utilizing some inequality techniques, It$\hat o$ formula and Borel-Cantelli Lemma, we show that the stochastic switched network model can achieve asymptotical synchronization in mean square, $H_\infty$-synchronization, and almost sure exponential synchronization when the delay of the control is smaller than a given upper bound. Finally, the effectiveness of the theory is verified by a numerical simulation.

Keywords

Delay feedback control / Markov switching / asymptotical synchronization in mean square / almost sure exponential synchronization / H_∞-synchronization