Extended Dissipativity Analysis for Delayed Markovian Jump Neural Networks via a Delay-Interval-Adjustable-Based Lyapunov-Krasovskii Functional

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.