Research On Exponential Synchronization Control For Switched Neural Networks With Mixed Time Delays

Exponential synchronization as a classical problem in dynamics, have foundapplications in the fields of mechanical, electrical, communications, and optics.Synchronization means that multiple chaotic or periodic system has a common dynamicbehavior. Chaotic system is extremely sharp to initial conditions, so it is conducive tomodern communication, such as secure communications, chaotic encryption, spreadspectrum communication, etc. To reasonable use of neural network system, it must havea given system to produce the synchronization orbit. Since1990, after the U.S. navy labPecora and Carrol observed synchronization phenomenon for the first time,synchronization becomes hotspot in the field of related problems. Neural networksynchronization become one of the important topics of the study. In this thesis, weconsider the exponential synchronization of switched neural network with mixed timedelays．The main results are as follows:Firstly, the problem of the exponential synchronization of switched coupled neuralnetworks with mixed time delays is studied. Through applying proper Lyapunovfunctional and some integral inequality techniques, a delay-dependent criterion is givento ensure the switched coupled neural networks with mixed time delays to beexponentially synchronization in terms of linear matrix inequalities (LMIs), then theswitched coupled neural networks is exponentially synchronize its isolated node.Secondly, we deal with the problem of exponential synchronization for neuralnetworks with mixed time delays and Markovian jump under sampled-data. Throughapplying a novel Lyapunov-Krasovskii functional and effective intermittent controller,sufficient conditions of exponential stability for error system, thus the neural networkswith mixed delays and markovian jump is proved to be exponentially synchronizationunder sampled-data, and both the existence conditions and the explicit characterization ofthe controller are derived in terms of LMIs. Finally, one illustrative example is given todemonstrate the validity of the proposed results.Finally, the exponential synchronization of stochastic neural networks with mixed delays and Markovian jump via sampled-data. Through constructing a novel Lyapunov–Krasovskii, the exponential stability for stochastic error neural networks with mixeddelays and Markovian jump under sampled-data is investigated, and a delay-dependentcriterion is given in terms of LMIs, thus the exponential synchronization for stochasticneural networks with mixed delays and Markovian jump via sampled-data is proved.