Quasi-Synchronization and Probability Distribution of Complex Networks With Semi-Markov Switched Coefficients

This article studies the almost sure quasi-synchronization and stochastic quasi-synchronization problems of complex networks with semi-Markov switched coefficients (SMSCs). Based on the distribution function and the generalized ergodic theory of semi-Markov process, a lemma is established to address the almost surely bounded convergence of the solution for semi-Markov switched systems (SMSSs), which is used to guarantee that the dynamical networks almost surely quasi-synchronize to a leader manifold. We also investigate the stochastic quasi-synchronization in the mean square for switched network systems with the help of the infinitesimal generator and the Lyapunov function. In addition, the probability distribution of the error systems with finite-state SMSSs is estimated. Meanwhile, an example is provided to validate the proposed theoretical results.