Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (2): 368-384.doi: 10.1016/S0252-9602(17)30008-5

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SYNCHRONIZATION OF MASTER-SLAVE MARKOVIAN SWITCHING COMPLEX DYNAMICAL NETWORKS WITH TIME-VARYING DELAYS IN NONLINEAR FUNCTION VIA SLIDING MODE CONTROL

M. Syed ALI1, J. YOGAMBIGAI1, Jinde CAO2,3   

  1. 1. Department of Mathematics, Thiruvalluvar University, Vellore 632115, Tamil Nadu, India;
    2. Department of Mathematics, Southeast University, Nanjing 210096, China;
    3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
  • Received:2015-09-16 Revised:2016-03-25 Online:2017-04-25 Published:2017-04-25

Abstract:

In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities (LMIs). Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin's formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

Key words: Markovian switching, complex dynamical networks, Lyapunov-Krasovskii method, sliding mode control, Linear Matrix Inequality

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