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在工程实际当中,时变时滞和不确定的存在往往使得系统的性能变差甚至不稳定。针对一类含混合变时滞的不确定中立系统,研究了时滞相关鲁棒稳定性问题。在考虑不确定性为泛数有界的条件下,首先通过构造包含三重积分项的Lyapunov-Krasovskii(L-K)的泛函,其次利用新的积分不等式更紧的界定条件,引入相关项自由权矩阵的方法,处理泛函沿系统的导数产生的交叉项,建立了基于线性矩阵不等式(LMI)形式的鲁棒稳定新判据。该方法不涉及复杂的模型变换,减小了理论推导和计算上的复杂性,所提出判据与离散时滞和中立时滞均相关,且扩大了系统稳定所允许的最大时滞上界范围,具有更低的保守性。仿真算例表明所提出的稳定性判据是有效的。
In engineering practice, the existence of time-varying delays and uncertainties often makes the performance of the system worse or even unstable. For a class of uncertain neutral systems with mixed time-varying delays, the robust stability problems with time-dependent delays are studied. Under the condition that the uncertainty is bounded by the bounded number, firstly, by constructing the functional of Lyapunov-Krasovskii (LK) containing triple integral terms, and secondly using the tighter bound conditions of the new integral inequalities, , A new robust stability criterion based on linear matrix inequality (LMI) is established by processing the cross terms of functional derivatives along the system. This method does not involve complex model transformation, reduces the theoretical derivation and computational complexity. The proposed criterion is related to both discrete delay and neutral delay, and enlarges the maximum delay upper bound allowed by system stability , With a lower conservative. Simulation results show that the proposed stability criterion is effective.