Almost sure exponential synchronization of multilayer complex networks with Markovian switching via aperiodically intermittent discrete observa- tion noise

This paper is concerned with almost sure exponential synchronization of multilayer complex networks with Markovian switching via aperiodically intermittent discrete observation noise. First, Markovian switching and multilayer interaction factors are taken into account simultaneously, which make our system more general compared with the existing literature. Meanwhile, the network architecture may be undirected or directed, and consequently, the adjacency matrix is symmetrical and asymmetrical. Second, the control strategy is based on aperiodically intermittent discrete observation noise, where the average control rate is integrated to depict the distributions of work/rest intervals of the control strategy from an overall perspective. Third, different from the work about $p$th moment exponential synchronization of network systems, by utilizing M-matrix theory and various stochastic analysis techniques including the Itô formula, the Gronwall inequality, and the Borel-Cantelli lemma, some criteria on almost sure exponential synchronization of multilayer complex networks with Markovian switching have been constructed and the upper bound of the duration time has been also estimated. Finally, several numerical simulations are exhibited to validate the effectiveness and feasibility of our analytical findings.