Delay Switch The Stability Of The Neural Network Analysis

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 regarded as linear or nonlinear systems, which are composed of a family of continuous-time or discrete-time subsystems and a rule that orchestrates the switching between the subsystems. In recent years, the switched neural networks, whose individual subsystems are a set of neural networks, have found their applications in the fields of high speed signal processing, artificial intelligence and other aspects. Therefore, researchers have studied the stability issues for the delayed switched Hopfield neural networks. Some stability conditions for switched Hopfield neural networks with time-varying delay are addressed based on the Lyapunov-Krasovskii functional approach. A switched neural network is usually called interval switched neural networks when the uncertainty is only due to the bounded deviations and perturbations of its parameters. The study on the stability of delayed interval switched neural networks becomes an important topic in theory and real applications. In this thesis, we consider the stability and state decay estimation problems for a class of delayed switched Hopfield neural networks. The main results are as follows:1) Delay-range-dependent global exponential stability and decay estimation for a class of switched Hopfield neural networks (SHNNs) of neutral type.The problem of delay-range-dependent global exponential stability and decay estima-tion for a class of switched Hopfield neural networks (SHNNs) of neutral type is studied. An average dwell time method is introduced into switched Hopfield neural networks. By constructing a new Lyapunov-Krasovskii functional and designing a switching law, some cri-teria are proposed to guarantee exponential stability for given system, while the exponential decay estimation is explicitly developed for the states. A numerical example is provided to demonstrate the effectiveness of the main results.2) Robust exponential stability problem for uncertain discrete-time switched Hopfield neural networks with time delay.We deal with the problem of robust exponential stability and decay estimation problem for uncertain discrete-time switched Hopfield neural networks with time delay. Firstly, the mathematical model of the uncertain discrete-time switched system is established. Then by constructing a new switching dependent Lyapunov-Krasovskii functional, some new delay-dependent criteria are developed, which guarantee the robust exponential stability of the uncertain discrete-time switched Hopfield neural networks. A numerical example is provided to demonstrate the effectiveness of the proposed algorithms.