具有非线性扰动的变时滞中立型系统鲁棒稳定性新判据

研究一类具有非线性扰动的时变时滞中立型系统鲁棒稳定性问题。基于直接Lyapunov Krasovskii泛函并结合自由权矩阵方法的分析方法，建立了线性矩阵不等式(LMI)形式的离散时滞和中立时滞均相关稳定性判据。与以往方法不同，在处理泛函导数时，该方法不包含任何模型变换和涉及交叉项的处理，只是通过引入相关项自由权矩阵，充分考虑各项之间的相互关系，降低了结论的保守性。最后，利用Matlab的LMI工具箱进行了的数值仿真, 算例仿真表明所提出的判据的有效性。

A new robust stability criterion for neutral systems with time-varying delays and nonlinear perturbation

The robust stability problem for neutral systems with time-varying delays and nonlinear perturbation is investigated. Based on the direct Lyapunov-Krasovskii functional approach and free weighting matrix technology, neutral and discrete delay-dependent stability criteria for the system are formulated in terms of Linear Matrix Inequalities (LMIs). Unlike some existing methodologies, when dealing with the time derivative of Lyapunov-Krasovskii functional, the proposed approach involves neither model transformation nor dealing with the cross-term, and only introduces some free weighing matrix for the correlation terms, in which the relationship between each terms is fully considered, and the less conservative robust stability criteria are proposed accordingly. At last, Matlab Toolbox LMI is used to perform some numerical simulations and the results demonstrate the effectiveness of the proposed stability criteria.