Research On Neutral Markovian Jumping System And Its Application In Complex Networks

With the rapid development of science and technology, the system scale is becom-ing larger and the phenomena are becoming more and more complex. Due to the great application of neutral Markovian jumping systems, they have received close attention by scholars at home and abroad. On the other hand, with the rapid improvement of com-puter technology and network theory, complex dynamic network has become a new hot topic. Since neutral delay and Markovian switching are always existed in large number of networks, then it is of great importance and significance to investigate these neutral Markovian jump complex networks. The main results obtained in this dissertation can be concluded as follows.1. The delay-range-dependent stochastic stability and exponential stabili-ty are investigated for the uncertain neutral Markovian jump systems with interval time-varying delays and nonlinear perturbations. A novel augment-ed Lyapunov functional which contains some triple-integral terms is intro-duced. Then by employing some integral inequalities and the nature of convex combination, some less conservative stochastic stability condition-s are presented in terms of linear matrix inequalities. Finally, numerical examples are provided to demonstrate the effectiveness and to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.2. The exponential stability is investigated for neutral Markovian jump sys-tems with interval mode-dependent time-varying delays, nonlinear pertur-bations and partially known transition rates. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservatism, then the exponential stability criteria are developed by Lyapunov stability theo-ry, reciprocally convex lemma and free-weighting matrices. Moreover, the corresponding results are extended to the uncertain case. Finally, numeri-cal examples are given to illustrate the effectiveness and superiority of the proposed criteria.3. The synchronization problem is investigated for a neutral complex dy-namical network with distributed delay, Markovian switching and partially unknown transition rates via sampled-data controller. A new augmented stochastic Lyapunov functional is constructed, which contains some triple-integral terms to reduce the conservativeness. Then the exponential stabili-ty conditions for the closed-loop error system are obtained by the Lyapunov stability theory, integral matrix inequalities and reciprocally convex lem-ma. Based on these new stability conditions, the sampled-data exponential synchronization controllers are found in terms of the solutions to linear ma-trix inequalities. Finally, numerical examples are given to demonstrate the feasibility and superiority of the proposed theoretic result.4. The finite-time synchronization problem is investigated for a class of neutral Markovian jumping complex networks with partly known transi-tion rates and mode-dependent delays. By utilizing the pinning control technique and constructing the appropriate stochastic Lyapunov functional, several sufficient conditions are proposed to ensure the finite-time synchro-nization for the neutral Markovian jumping complex dynamical networks, based on the Kronecker product, inequality techniques and finite-time sta-bility theorem. Finally, numerical examples and simulations are given to illustrate the feasibility and superiority of the proposed results.5. It is concerned with the synchronization problem for a class of Marko-vian jump complex heterogeneous networks with partly unknown transition rates and time-varying delay. Based on the concept of quasi-synchronization, a novel stochastic Lyapunov functional is constructed to solve the problem. Then two sufficient quasi-synchronization conditions are presented, and ex-plicit expressions of error levels are proposed to estimate the synchroniza-tion error. Finally, numerical examples are provided to demonstrate the feasibility and effectiveness of the proposed theoretic results.