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研究一类区间时变时滞线性不确定系统的鲁棒稳定性问题.通过引入增广Lyapunov泛函,结合积分不等式方法,导出了区间时变时滞线性系统的时滞相关鲁棒稳定性新判据.与现有方法不同,该方法不涉及自由权矩阵技术和任何模型变换,减少了理论和计算上的复杂性,而且在估计Lyapunov泛函导数的上界时没有忽略某些有用项.数值算例表明,所提出的判据是有效的,具有更低的保守性.
In this paper, we study the robust stability of a class of linear uncertain systems with time-varying delay in the interval. By introducing the augmented Lyapunov functional and the method of integral inequality, the delay-dependent robust stability of linear systems with time-varying delay is derived. Unlike existing methods, this method does not involve the free-weight matrix technique and any model transformation, reduces the theoretical and computational complexity, and does not neglect certain useful items in estimating the upper bound of Lyapunov functional derivatives. Numerical examples show that the proposed criterion is effective and has a lower conservativeness.