Robust exponential synchronization of a Markovian jump complex dynamical network with piecewise homogeneous Markovian parameters

Abstract

Abstract This paper establishes a stochastic synchronization method for a Markovian jump complex dynamical network (MJCDN) with time-delay and uncertainties. The considered Markovian structure is piecewise-homogeneous with piecewise-constant time-varying transition rates (TRs). Two Markovian signals are utilized to construct the piecewise-homogeneous Markovian structure. A low-level Markovian signal with time-varying TRs governs the switching between the system dynamics while it is managed by a high-level Markovian signal. Due to the effect of imperfections induced by modeling errors in the system dynamics, some parametric norm-bounded uncertainties are considered. In addition, uncertain TR matrix is considered which means that inaccurate or uncertain information for each element of the TR matrix is allowable. This modelling makes the MJCDN to be more general and applicable than the existing ones. Synchronization conditions are obtained and reported in the form of linear matrix inequalities by the help of Lyapunov–Krasovskii theory, Wirtinger-based integral inequality approach and reciprocally convex technique. Finally, a numerical example is presented to verify the effectiveness of the proposed method.