Dynamics Of Switched Systems With Time Delay And Its Applications In Memristor-Based Neural Networks

Many physical and engineering systems in real world need to be described by switched system. Switched systems, as a special case of hybrid systems, which are composed of a fam-ily of continuous-time or discrete-time subsystems and a rule that orchestrates the switching between the subsystem. Recently, dynamic behavior of switched systems has become a hot topic and received much attention from all over the world. Especially, memristor-based neural networks model can be seen as a special switched systems, whose switching rule depends on the state of networks. Memory characteristic of memristor is an ideal component to imitate neuron synapse, hence, the research on memristor-based neural networks have both great theo-retical values and practical applications. Based on the theory of switched systems, differential inclusion theory, Lyapunov stability theory, functional differential equations, as well as control theory, Halanay inequality, generalized Halanay inequality, and w-matrix measure, this disser-tation addresses robust stability, state estimation, passivity, exponential synchronization and synchronization control problems for switched interval neural networks with time delay and switched coupled interval neural networks with time delay. Finally, the adaptive synchroniza-tion and lag quasi-synchronization problems for memristor-based neural networks with time delay are considered. This dissertation is divided into six chapters, the main contents can be summarized as follows:In the first chapter, the significance and the development tendency of switched systems, neural networks and memristor-based neural networks together with current research situation are briefed. The main contents and the main contributions of this dissertation are also stated according to the above mentioned analysis.In the second chapter, state estimation and robust stability of switched neural networks with time delay and interval uncertain parameters (switched interval neural networks with time delay) are investigated. In Section 2.1, the development of switched interval neural networks with time delay and actuality of state estimation of neural networks with time delay are briefed. In Section 2.2, based on state estimation theory, state estimation for switched interval neural networks with time delay is considered. By employing average dwell time method, Lyapunov functional and designing proper state estimator with full dimensions, some delay-dependent criteria are obtained to guarantee exponential robust stability for estimation error system. In Section 2.3, by using piecewise analysis method, the stability of switched interval neural networks with fast-varying or slow-varying interval time delay and state-dependent switching rule are addressed. Combing the completeness of matrix, switching rule depending on the state of neural networks is designed, some new criteria for guaranteeing robust stability of switched interval neural networks with time delay are derived in terms of linear matrix inequalities.In the third chapter, the problem of synchronization for switched interval neural networks with time delay and intermittent controller is discussed. By using ω-matrix measure and Halanay inequality technique, designing proper intermittent control strategy, some algebraic criteria are derived for exponential synchronization of switched interval neural networks with time delay under arbitrary switching rule, complex Lyapunov functional can be avoided in this method.In the forth chapter, the synchronization and passivity of switched coupled interval neu-ral networks are discussed. In Section 4.1, the development of coupled neural networks is introduced. In Section 4.2, the synchronization of switched coupled interval neural networks with intermittent control is considered, by using Halanay inequalities, and combing multiple Lyapunov functional, new synchronization criteria are obtained for switched coupled interval neural networks under intermittent control. In Section 4.3, passivity of switched coupled inter-val neural networks with asymmetric coupling topology, Lyapunov function can be seen as the energy function, the passivity results are derived for switched coupled interval neural networks with asymmetric coupling, and reveal the relationship between passivity and synchronization. Furthermore, synchronization criteria can be obtained from passivity results.The fifth chapter, the problem of synchronization for memristor-based neural networks is considered. In Section 5.1, synchronization for memristor-based neural networks with time delay via adaptive controller and feedback controller is investigated. Under the framework of Filippov’s solution and differential inclusion theory, adaptive updated law is designed, two kinds of synchronization criteria for memristor-based neural networks with time-varying delay are derived. Numerical simulation shows the solutions of memristor-based neural networks strictly depend on the initial condition. In Section 5.2, by using discontinuous controller, anti-synchronization criteria for memristor-based neural networks are given. In Section 5.3, lag quasi-synchronization problem of memristor-based coupled neural networks with parameter mismatch is considered, based on the ω-measure method and generalized Halanay inequali-ty, the error level is explicitly estimated, and the relationship among parameter mismatch, feedback matrix and synchronized error is also given. Moreover, by constructing Lyapunov functional, several lag synchronization criteria for the memristor-based neural networks are given, which depend on the switching parameters. Hence, the proposed results in this chapter have less conservativeness.In the sixth chapter, the work of this dissertation is summarized. Furthermore, the prospect for the future work is made.