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Improved Delay-Dependent Stability and Stabilization Conditions of T-S Fuzzy Time-Delay Systems via an Augmented Lyapunov-Krasovskii Functional Approach

机译：通过增强Lyapunov-Krasovskii功能方法改善T-S模糊时滞系统的延迟依赖性稳定性和稳定条件

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摘要

This paper develops some improved stability and stabilization conditions of T-S fuzzy system with constant time-delay and interval time-varying delay with its derivative bounds available, respectively. These conditions are presented by linear matrix inequalities (LMIs) and derived by applying an augmented Lyapunov-Krasovskii functional (LKF) approach combined with a canonical Bessel-Legendre (B-L) inequality. Different from the existing LKFs, the proposed LKF involves more state variables in an augmented way resorting to the form of the B-L inequality. The B-L inequality is also applied in ensuring the positiveness of the constructed LKF and the negativeness of derivative of the LKF. By numerical examples, it is verified that the obtained stability conditions can ensure a larger upper bound of time-delay, the larger number of Legendre polynomials in the stability conditions can lead to less conservative results, and the stabilization condition is effective, respectively.
机译：本文开发了T-S模糊系统的一些提高稳定性和稳定条件，其具有恒定的时滞和间隔时变延迟，分别具有其衍生界的可用。这些条件通过线性矩阵不等式（LMI）呈现，并通过应用增强的Lyapunov-Krasovskii功能（LKF）方法来结合规范贝塞尔 - Legendre（B-L）不等式。不同于现有的LKFS，所提出的LKF涉及更多的状态变量，以增强方式求助于B-L不平等的形式。 B-L不平等也适用于确保构建的LKF的正力和LKF的衍生物的否定性。通过数值示例，验证所获得的稳定性条件可以确保较大的时滞的上限，稳定条件中的较大数量的legendre多项式可以导致较少的保守结果，并且稳定条件分别是有效的。

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  • 来源
    《Mathematical Problems in Engineering》 |2019年第15期|30.1-30.12|共12页
  • 作者

    Gao Zifan; Yang Jiaxiu; Zhu Shuqian;

  • 作者单位

    Shanxi Univ Sch Math Sci Taiyuan 030006 Shanxi Peoples R China;

    Shanxi Univ Sch Math Sci Taiyuan 030006 Shanxi Peoples R China;

    Shandong Univ Sch Math Jinan 250100 Shandong Peoples R China;

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