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Improved results on nonlinear perturbed T–S fuzzy systems with interval time-varying delays using a geometric sequence division method

机译：时变时滞非线性扰动TS模糊系统几何序列划分方法的改进结果

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摘要

This paper presents improved stability results by introducing a new delay partitioning method based on the theory of geometric progression to deal with T–S fuzzy systems in the appearance of interval time-varying delays and nonlinear perturbations. A common ratio α is applied to split the delay interval into multiple unequal subintervals. A modified Lyapunov–Krasovskii functional (LKF) is constructed with triple-integral terms and augmented factors including the length of every subintervals. In addition, the recently developed free-matrix-based integral inequality is employed to combine with the extended reciprocal convex combination and free weight matrices techniques for avoiding the overabundance of the enlargement when deducing the derivative of the LKF. Eventually, this developed research work can efficiently obtain the maximum upper bound of the time-varying delay with much less conservatism. Numerical results are conducted to illustrate the remarkable improvements of this proposed method.
机译：本文介绍了一种基于几何级数理论的新型延迟分配方法，以解决区间时变时滞和非线性扰动下的TS模糊系统，从而提高了稳定性。应用公共比率α将延迟间隔分为多个不相等的子间隔。修改后的Lyapunov–Krasovskii函数（LKF）由三重积分项和包括每个子区间的长度在内的增强因子构成。此外，最近开发的基于自由矩阵的积分不等式与扩展的倒数凸组合和自由权重矩阵技术结合使用，可避免推导LKF导数时出现过多的扩大。最终，这项发达的研究工作可以有效地获得时变延迟的最大上限，而保守性却要低得多。数值结果表明了该方法的显着改进。

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