Finite-Time Quasi-Synchronization of Stochastic Multilayer Networks With Energy Consumption Estimation

Abstract

The control cost is an important and inevitable problem for network control. In existing work on finite-time (FnT) synchronization on stochastic multilayer networks (MNs), the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th moment synchronization based on energy consumption estimation has not been involved. This brief firstly proposes two new FnT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th moment quasi-stability theorems of stochastic systems, which expand the existing value range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> . Second, novel sufficient criteria are obtained for FnT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th moment quasi-synchronization of stochastic MNs. Compared with some existing FnT synchronization of stochastic MNs, this brief not only gives the range of the number of layers about MNs under the minimum convergence time, but also gives the estimation of energy consumption. Finally, numerical simulation shows that the theoretical analysis is effective.