时滞切换神经网络的稳定性分析
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摘要
随着智能控制的发展,混杂系统得到了更广泛的应用.作为一种特殊的混杂系统,切换系统是由一族连续时间或离散时间子系统和描述它们之间联系的切换规则所组成的线性或非线性系统.近年来,由一系列神经网络子系统所构成的切换神经网络被应用到高速信号处理和人工智能等领域.因此，人们对时滞切换Hopfield神经网络的稳定性问题进行了研究,并基于Lyapunov-Krasovskii泛函方法得到了一些稳定性条件.区间时滞切换神经网络是参数在某一有界区间内变化的切换神经网络系统,研究区间时滞切换神经网络的稳定性在理论和实践上都具有十分重要的意义.该论文主要针对时滞切换神经网络系统的稳定性及状态衰减估计问题做了一些理论性的研究.其主要结果包括以下两个部分：
1)中立型区间时变时滞切换Hopfield神经网络的指数稳定性分析和状态衰减估计.
研究中立型区间时变时滞切换Hopfield神经网络的全局指数稳定性和状态衰减估计的问题.基于Lyapunov-Krsasovskii稳定性理论和线性矩阵不等式技术,构造新的Lyapunov泛函,应用平均驻留时间方法对中立型区间时变时滞切换Hopfield神经网络系统,给出时滞依赖渐近稳定性条件和状态衰减估.所给这些充分条件均以线性矩阵不等式的形式给出,容易验证.仿真结果进一步证明结论的有效性.
2)不确定离散时间时滞切换Hopfield神经网络的鲁棒指数稳定性.
针对离散时间时滞不确定切换Hopfield神经网络系统考虑其鲁棒指数稳定性及状态衰减估计问题.首先给出不确定离散时间时滞切换Hopfield神经网络的模型,再应用有限和不等式技术和平均驻留时间方法,通过建立一个新的Lyapunov泛函得到几个时滞依赖条件,使其确保所考虑的不确定离散时间切换Hopfield神经网络鲁棒指数稳定.最后通过数值例子验证了方法的有效性.
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.
1)中立型区间时变时滞切换Hopfield神经网络的指数稳定性分析和状态衰减估计.
研究中立型区间时变时滞切换Hopfield神经网络的全局指数稳定性和状态衰减估计的问题.基于Lyapunov-Krsasovskii稳定性理论和线性矩阵不等式技术,构造新的Lyapunov泛函,应用平均驻留时间方法对中立型区间时变时滞切换Hopfield神经网络系统,给出时滞依赖渐近稳定性条件和状态衰减估.所给这些充分条件均以线性矩阵不等式的形式给出,容易验证.仿真结果进一步证明结论的有效性.
2)不确定离散时间时滞切换Hopfield神经网络的鲁棒指数稳定性.
针对离散时间时滞不确定切换Hopfield神经网络系统考虑其鲁棒指数稳定性及状态衰减估计问题.首先给出不确定离散时间时滞切换Hopfield神经网络的模型,再应用有限和不等式技术和平均驻留时间方法,通过建立一个新的Lyapunov泛函得到几个时滞依赖条件,使其确保所考虑的不确定离散时间切换Hopfield神经网络鲁棒指数稳定.最后通过数值例子验证了方法的有效性.
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.
引文
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