Exponential synchronization of a Markovian jump complex dynamic network with piecewise-constant transition rates and distributed delay

Abstract

The exponential synchronization of a Markovian jump complex dynamical network with piecewise-constant transition rates is investigated. Two distinct types of time-varying delay are considered for the system; one is distributed time-delay for each node, the other is discrete coupling time-delay. Based on an augmented Lyapunov–Krasovskii functional, some sufficient conditions are derived and expressed in the form of linear matrix inequalities, which are formulated in such a manner as to determine the controller gain matrices. Finally, an example is given to illustrate the effectiveness and validity of the proposed method.

Keywords

Complex dynamic network Lyapunov–Krasovskii theory synchronization piecewise homogeneous Markovian parameters time-delay

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