Research On Robust Stability And State Estimation For Switched Interval Neural Networks With Time Delays

With the rapid development of intelligent control, hybrid systems have been investigated for their extensive applications. As a special class of hybrid systems, switched systems are composed of a family of continuous-time or discrete-time subsystems. Recently, switched neural networks, whose individual subsystems are a set of neural networks, have found applications in fields of high speed signal processing, artificial intelligence, and gene selection. Therefore, some researchers have studied the stability issues for switched neural networks. In this thesis, we consider the robust stability and state estimation problems for a class of switched interval neural networks. The main results are as follows:Firstly, the problem of robust stability of switched interval neural networks with discrete and distributed time-varying delays of neural type is studied. By applying the augmented Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) techniques, a delay-dependent criterion is achieved to ensure to such switched interval neural networks to be globally asymptotically robustly stable in terms of LMIs.Secondly, we deal with the problem of Switched exponential state estimation and robust stability for interval neural network with discrete and distributed time delays, by applying the augmented Lyapunov-Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay-dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.Thirdly, based on the strictly complete property of the matrices system, a switching rule which depends on the state of the network, the switched generalized neural networks is designed, and a novel Lyapunov-Krasovskii function is employed to investigate the exponential stability for the switched generalized neural networks under the state-depend ent switching rule. A delay-dependent criterion is achieved in terms of Linear matrix inequalities (LMIs), which guarantees the exponential stability for the switched neural networks.