Improved Stabilization for Continuous Dynamical Systems with Two Additive Time‐Varying Delays

This paper studies the problem of stabilization criteria for systems with two additive time‐varying delays. First, the delay‐dependent stability condition for the systems is established through computing the more general Lyapunov functional. The Lyapunov functional is constructed by making full use of the property and the information of the systems, and the condition has advantages over the existing ones in the skillful combination of the delay decomposition and the reciprocal convex approach. Second, considered to be more flexible for the controller design with the introduced positive scalar, a new controller method is presented. Finally, two examples are provided to demonstrate the advantage of the results in this paper.     

Stochastic stability analysis for neutral-type Markov jump neural networks with additive time-varying delays via a new reciprocally convex combination inequality

This paper investigates the stochastic stability problem for a class of neutral-type Markov jump neural networks with additive time-varying delays. Firstly, to derive a tighter lower bound of the reciprocally convex quadratic terms, a new reciprocally convex combination inequality is established by using parameters transformation approach. Secondly, by fully considering the peculiarity of various time-varying delays and Markov jumping parameters, an eligible stochastic Lyapunov–Krasovskii functional is constructed. Then, by employing the new reciprocally convex combination inequality and other analytical techniques, some novel stability criteria are provided in the forms of linear matrix inequalities. Finally, four illustrated examples are given to verify the effectiveness and feasibility of the proposed methods.     

具反应扩散混合时滞Cohen-Grossberg神经网络的指数耗散性

利用扩散算子特性、M-矩阵性质和不等式分析技巧,在不要求神经网络激励函数的有界性、单调性、可微性以及平均时滞有界性的弱保守条件下,研究了一类具有反应扩散混合时滞的非自治Cohen-Grossberg神经网络的实不变集、全局指数稳定性和指数耗散性,并给出了相关的充分性条件.文中所使用的方法摒弃了常规构造适当的Lyapunov泛函的方法,克服了Lyapunov泛函难构造的困难,且得到的结果扩展和改进了其他文献结果.最后给出了一个数值例子来说明所得结果的有效性.     

Global Robust Exponential Stability of Interval General BAM Neural Network with Delays

In this paper, a class of interval general bidirectional associative memory (BAM) neural networks with delays are introduced and studied, which include many well-known neural networks as special cases. By using fixed point technic, we prove an existence and uniqueness of the equilibrium point for the interval general BAM neural networks with delays. By using a proper Lyapunov functions, we get a sufficient condition to ensure the global robust exponential stability for the interval general BAM neural networks with delays, and we just require that activation function is globally Lipschitz continuous, which is less conservative and less restrictive than the monotonic assumption in previous results. In the last section, we also give an example to demonstrate the validity of our stability result for interval neural networks with delays.     

Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for discrete-time stochastic neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, the delay-dependent robust dissipativity criteria are also presented. Two examples are given to show the effectiveness and less conservatism of the proposed criteria.     

Synchronization for an array of coupled stochastic discrete-time neural networks with mixed delays

In this paper, a synchronization problem is investigated for an array of coupled stochastic discrete-time neural networks with both discrete and distributed time-varying delays. By utilizing a novel Lyapunov function and the Kronecker product, it is shown that the addressed stochastic discrete-time neural networks is synchronized if certain linear matrix inequalities (LMIs) are feasible. Neither any model transformation nor free-weighting matrices are employed in the derivation of the results obtained, and they can be solved efficiently via the Matlab LMI Toolbox. The proposed synchronization criteria are less conservative than some recently known ones in the literature, which is demonstrated via two numerical examples.     

Multiple asymptotical stability analysis for fractional-order neural networks with time delays

This paper formulates the multiple asymptotical stability for a general class of fractional-order neural networks with time delays. By exploiting the properties of upper bounded and lower bounded functions derived from the addressed fractional-order neural network model as well as the comparison principle for fractional-order calculus, a lot of sufficient conditions are obtained to guarantee the existence and multiple asymptotical stability of the equilibrium points for the fractional-order neural networks with time delays. It reveals that the results gained in this paper are applicable to analyses of both multiple asymptotical stability and global asymptotical stability. Besides, three numerical examples are presented to showcase the validity of the derived results.     

Global Robust Exponential Stability of Interval BAM Neural Network with Mixed Delays under Uncertainty

In this paper, a class of interval bidirectional associative memory (BAM) neural networks with mixed delays under uncertainty are introduced and studied, which include many well-known neural networks as special cases. The mixed delays mean the simultaneous presence of both the discrete delay, and the distributive delay. Furthermore, the parameter of matrix is taken values in a interval and controlled by a unknown, but bounded function. By using a suitable Lyapunov–Krasovskii function with the linear matrix inequality (LMI) technique, we obtain a sufficient condition to ensure the global robust exponential stability for the interval BAM neural networks with mixed delays under uncertainty, which is more generalized and less conservative, restrictive than previous results. In the last section, the validity of our stability result is demonstrated by a numerical example.     

An improved stability result for linear time-delay system using a new Lyapunov–Krasovskii functional and extended reciprocally convex inequality

This paper is concerned with the stability analysis of a linear system with interval time-varying delay using an augmented Lyapunov–Krasovskii (LK) functional approach. A delay-dependent stability criterion is developed in LMI framework to estimate the maximum allowable bound of the time-delay within which the system remains asymptotically stable in the sense of Lyapunov. Conservatism in the proposed delay-dependent stability analysis is reduced by introducing a new LK functional along with the Wirtinger's inequality and extended reciprocally convex matrix inequality. Finally, two numerical examples and the load frequency control problem have been solved to validate the superiority of the proposed stability criterion compared to existing literature.