Study On Stability And Synchronization Problems Of Markov Switching Complex Networks

With the development of science and technology, our daily life is increasingly dependent on complex dynamical networks, such as the Internet, communication net-works, and social networks, and so on. Over the last decade, because complex dynam-ical networks consist of a large number of dynamical nodes and nodes have diversity, complex dynamical networks have been intensively studied in various disciplines, such as mathematics, biology, engineering, and social science. Therefore, the study of com-plex dynamical networks is of great necessary for us. Network stability is one of the most basic and necessary conditions to ensure network security and reliability. More-over, Synchronization in complex dynamical networks, as one of the most important collective behaviors, has potential applications in many fields including secure commu-nization, parallel image processing, neural networks, information science, etc.In the thesis, stability and synchronization problems are investigated for Markov switching complex dynamical networks. At first, stabilization and synchronizability problems are analyzed for the mixed time-delays discrete time Markov jump complex networks with packet losses. Next, finite-time cluster synchronization problem is dis-cussed for the delayed Markov switching complex networks with disturbance. Then, we discuss the finite-time synchronization of Markov switching delayed complex networks with partially unknown transition rates. And then dissipativity and robust stability problems are studied for Markov switching unknown singular systems with mixed time delays. Finally, consensus problem of the second-order sampling data multi-agents sys-tems with packet losses is investigated. The compendious frame and description of the thesis are given as follows:(1) Stabilization and synchronization of Markov jumping discrete-time complex networks with mixed time delays. Stability and synchronization prob-lems of Markov jumping complex networks with mixed time delays and packet losses are investigated in detail. Compared with the previous work, both mixed time de-lays, packet losses and quantization error phenomenons are considered. By utilizing packet losses compensation and quantization control method, the conditions are given to ensure the stability and synchronization of the discrete-time complex networks with mixed time delays. Finally, simulation examples are given to illustrate the effectiveness of the developed theoretical results.(2) Finite-time cluster synchronization of Markov switching complex networks with time delays and random disturbance. A general model of Markov switching complex networks with time delays and random disturbance is proposed. And finite-time cluster synchronization of the addressed complex networks is studied. Com-pared with the previous work, the proposed model contains the time delays and ensures the nodes to reach synchronization respectively in each cluster. By constructing the suitable controllers and the stochastic Lyapunov-Krasovskii functional, we derive the conditions of the finite-time cluster synchronization for the addressed complex net-works. Finally, numerical examples are provided to demonstrate the effectiveness and the applicability of the proposed method.(3) Finite-time synchronization of Markov switching complex networks with partially unknown transition rates. By using the finite-time stability the-orem, finite-time synchronization problem is investigated for Markov switching com-plex networks with partially unknown transition rates. Compared with the references on the synchronization of complex networks with partially unknown transition rates, finite-time synchronization problem is considered based on the proposed model. And compared with the works on the finite-time synchronization of the time-delay com-plex networks, these references investigated the finite-time boundedness problems, we studied the problems of finite-time convergence for the error systems. Then we de-duce the criteria of the finite-time stability of error systems by using the finite-time stability theorem, and ensure the finite-time synchronization of the addressed complex networks. Finally, numerical simulations illustrated to verify the effectiveness of the proposed results.(4) Dissipativity analysis and robust stability of Markov jump singular systems with mode-dependent mixed time-delays. The delay-dependent dissi-pativity analysis and robust stability problems are investigated for Markov jump sin-gular systems with mode-dependent mixed time-delays. By using the novel Lyapunov-Krasovskii functional and stochastic analysis theory, the new criteria are derived to guarantee that the addressed singular systems are stochastically admissible, robust sta-bility and strictly (Q, R,S)-a-dissipativity, the obtained conditions are delay-dependent. Numerical examples are presented to illustrate the effectiveness and less conservative-ness of the proposed theoretical results.(5) Consensus of second-order sampled-data multi-agent systems with packet losses. The consensus problem is considered for second-order sampled-data multi-agent systems with packet losses. A Bernoulli stochastic variable is used to char-acterize the packet loss phenomenon of second-order sampled-data multi-agent sys-tems, and the new model of second-order multi-agent systems is proposed. Several sufficient conditions are given to ensure the almost surely consensus by using system discretization method and stochastic control theory. Finally, we apply the developed results to the coordination of multiple vehicles. Two examples are provided to illustrate the effectiveness of our results.