Extended Dissipativity Analysis for Delayed Markovian Jump Neural Networks via a Delay-Interval-Adjustable-Based Lyapunov-Krasovskii Functional
提出一种延迟区间可调的李雅普诺夫-克拉索夫斯基泛函，用于分析延迟马尔可夫跳跃神经网络的扩展耗散性，通过数值例子和四水箱过程系统验证了方法的有效性，可应用于电力系统稳定控制、机器人运动控制和图像处理。
The issue of extended dissipativity analysis (EDA) for delayed Markovian jump neural networks (MJNNs) is investigated in this article. First, a delay-interval-adjustable-based Lyapunov-Krasovskii functional (LKF) is proposed, in which the delay interval is adjusted by a tunable parameter to obtain an optimal extended dissipativity result, offering a new idea to enhance the consideration of delay information. Furthermore, to take into account more effective information, the LKF is augmented with both single and quadratic integral variables. Accordingly, the LKF derivative becomes a higher-order term of the time-varying delay. To solve this nonlinear problem, a variable-augmented-based free-weighting-matrices approach is employed to transform the nonlinear term into a linear form and provides more freedom in obtaining enhanced EDA results. Then, two novel extended dissipativity criteria of delayed MJNNs are derived. Meanwhile, to show the general applicability of the proposed methods, the derived criteria are applied to the EDA and stability analysis for delayed neural networks (NNs). Lastly, the merits and effectiveness of the proposed techniques are demonstrated through three numerical examples and a real-world application of a quadruple-tank process system. Additionally, the proposed methods can be effectively applied to the practical fields of power system stability control, robot motion control, and image processing, while reducing the conservatism of system performance results.