含分布时滞的不确定中立系统鲁棒稳定之时滞分解法

DELAY-DECOMPOSITION APPROACH FOR THE ROBUST STABILITY OF UNCERTAIN NEUTRAL SYSTEMS WITH DISTRIBUTED DELAYS

研究了一类同时具有离散与分布时滞的不确定中立型系统的鲁棒稳定性问题,基于时滞分割方法建立一种新的时滞相关鲁棒稳定性条件.通过把时滞区间非均匀的分解成N份,针对不同的分割区间构造合适的Lyapunov-Krasovskii(L-K)泛函,结合积分不等式处理方法建立了基于线性矩阵不等式(LMI)形式的时滞相关条件,该方法不包含任何的模型变换和自由权矩阵技术,减少了理论与计算上的复杂性,最后的数值算例仿真表明,该方法扩大了系统稳定的时滞上界范围,相比已有结论具有更低的保守性.

This paper deals with the problem of robust stability of uncertain neutral systems with distributed delays. A new delay-dependent stability condition is derived by using the delay-decomposition approach. Firstly, by non-uniformly dividing the delay interval into N segments, a new appropriate Lyapunov-Krasovskii （L-K） func~ tional for each segment is constructed. Then, with the integral inequality approach, a new delay-dependent stability condition is formulated in terms of linear matrix inequalities. The proposed approach involves neither model transformation nor free~ weighting matrix, so the complexity is reduced both in theory and in computation. Numerical examples show that the proposed method enlarge the more conservative upper bound for the delay-range.