Research On Robust Fault-tolerant Synchronization For Complex Dynamical Networks Based On Sample-data Control

Complex dynamical networks(CDNs) have become a hot research topic in recent years and received a great deal of attention since they are revealed to extensively exist in various fields of real world. Based on the previous studies, and by using the knowledge of the matrix analysis, Lyapunov stability theory, stochastic analysis method, the dissertation is concerned with the synchronization control problem for complex dynamical networks which includes: synchronization analysis, faulttolerant control and analysis, mixed H∞/passive control and sample-data control. The main results are given as follows:(1) The problem of mixed H∞/passive fault-tolerant synchronization for complex dynamical networks with time-varying delayed couplings via a sampled-data control scheme is investigated. The purpose is focused on designing controller such that the resulting synchronization error system is stable and a mixed H∞/passive performance level is satisfied. Based on the input delay approach and by using some new tools to deal with the Lyapunov functional, a sufficient condition which ensures the existence of the desired sampled-data controller is presented. Based on the condition, an explicit expression for the desired controller is given. Finally, three examples are employed to demonstrate the effectiveness and the reduced conservatism of the proposed method.(2) The fault-tolerant mixed H∞/passive synchronization problem for chaotic neural networks by sampled-data control scheme is addressed. The objective is focused on the design of a reliable controller such that the mixed H∞/passive performance level of the resulting synchronization error system is ensured in the presence of actuator failures. A time-dependent Lyapunov functional and an improved reciprocally convex approach combined with a novel integral inequality are applied to optimize the availability of the information on the actual sampling pattern. Then, some sufficient conditions of mixed H∞/passive performance analysis for the synchronization error systems are derived. A desired reliable sampled-data controller is designed by solving the optimization problems. Finally, to demonstrate the effectiveness of the proposed method, a practical chaotic neural networks is provided.(3) The robust fault-tolerant synchronization control for CDNs based on a Markov model is considered here. The main aim is to design a sampled-data controller which the fault-tolerance and dissipativity are also taken into account and ensure that the error system is asymptotically stable and simultaneously satisfies a dissipative property in the presence of the actuator failures. First, based on the input delay approach, by choosing a Markov switched Lyapunov functional and adopting some new tools to deal with the Lyapunov functional, a sufficient condition which ensures the existence of the desired sampled-data controller is presented. Then, an explicit expression for the desired sampled-data controller is given by a simple matrix decoupling approach. A criterion ensuring the dissipativity property of CDNs is also established. Based on this, the H∞, passive and mixed H∞/passive problem for CDNs are also obtained in a unified frame by turning some fixed parameters. Finally, an example is employed to demonstrate the effectiveness of the proposed method.