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Synchronization Analysis And Control Of Nonlinear Systems With Impulsive Effect

Posted on:2016-11-09Degree:DoctorType:Dissertation
Country:ChinaCandidate:G Z FengFull Text:PDF
GTID:1108330503477525Subject:Control theory and control engineering
Abstract/Summary:PDF Full Text Request
Nonlinear system dynamics is content-richer than linear system. In practice, the model abstracted from a variety of movement is essentially nonlinear, such as chaotic systems, nonlin-ear coupling complex networks, etc. Due to the complexity and wide application of nonlinear network system, they have become hot research topics. Synchronization of complex networks and chaotic systems is one of the important research topics. On the other hand, the theory of impulsive control has been widely applied in many fields because of its unique advantages. Therefore, how to use impulse control theory to realize synchronization of complex networks and chaotic systems has become the current hot research subject. By using Lyapunov sta-bility theory, the theory of impulsive differential system and linear matrix inequality (LMI) method, we discussed synchronization of nonlinear coupled complex system with impulsive con-trol, master and slave synchronization of chaotic systems with modified impulsive controller, E-exponential stability and exponential stability of singular and switched systems. The main contents of this dissertation can be summarized as follows:(1) For synchronization problem of nonlinearly-coupled dynamical networks, an effective-ly impulsive control scheme is proposed to synchronize the network onto the objective state. The internal coupling matrix is symmetric or asymmetric. Based on the stability analysis of impulsive differential equations, a low-dimensional sufficient condition is derived to guaran-tee the exponential synchronization by virtue of average impulsive interval which reduce the conservation of the known results.(2) For global exponential synchronization of chaotic systems by designing a novel im-pulsive controller. The novel impulsive controller is a combination of the current and past error states, which is a modification of the normal impulsive one. Some global exponential stability criteria are derived for the error system by utilizing the stability analysis of impulsive differential equations and differential inequalities, and moreover, the exponential convergence rate can be specified. By using such a technique, we can increase the impulse distances, and reduce the control cost.(3) Applying the Lyapunov functional method, we deal with the effects of delayed im-pulses on exponential stability of impulsive time-delay systems. Under certain conditions, the exponential stability of time-delayed systems is robust with respect to sufficiently small im-pulse input delays. Irrespective of the sizes of the impulse input delays, time-delayed systems is exponential stable when the magnitude of the delayed impulses is sufficiently small and the impulse input delays satisfies the average impulsive interval. We applied our Lyapunov-based results to a class of nonlinear impulsive time-delay systems.(4) For E-exponential stability problems of hybrid impulsive and switching singular sys-tems. Using switching Lyapunov functions and algebraic inequality, sufficient conditions ex-pressed as arbitrary and conditioned impulsive switching are obtained. In addition, with introduction of the impulsive controller, several exponential stability criteria are derived when the considered singular systems are regular and impulse free.(5) By employing Lyapunov functional method and linear matrix inequalities (LMIs), the asymptotical stability is studied for the coupled delayed neural networks. Furthermore, we presented a newly neural network model including both intrinsic disturbance of single node and communication noise over the network connections, only one controller is used for the stabilization of the neural networks in terms of LMIs, and the prescribed performance constraint is satisfied. The proposed linear matrix inequality results are easy to be solved by standard commercial software. In addition, the coupling network can be a undirected graph can also be a directed graph. As you can see, the design of single controller saves cost control, enriches the existing control neural network research.
Keywords/Search Tags:Complex networks, Chaotic systems, Nonlinear systems, Impulsive control, Master system, Slave system, Nonidentical systems, Synchronization, Pinning control
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