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研究了一类具有区间时变时滞的不确定离散时间系统的鲁棒稳定性问题。首先,将时滞区间分成两个子区间,在不同的子区间上通过构造不同的Lyapunov泛函,再结合一个更紧的不等式,在没有忽略任何有用项的前提下,得到了基于线性矩阵不等式形式的时滞相关的稳定性判据。证明过程既没有利用模型变换也没有引进自由权矩阵,降低了结论的保守性和计算量。数值算例说明了该方法的有效性。
The problem of robust stability for a class of uncertain discrete-time systems with time-varying intervals is investigated. First, we divide the time-lag interval into two sub-intervals. By constructing different Lyapunov functional in different sub-intervals and combining with a tighter inequality, we obtain the linear matrix inequality based on the linear matrix inequality without neglecting any useful term. Delay-related stability criteria. Proving that the process neither uses model transformation nor introduces the matrix of free weights reduces the conservation and computation of the conclusion. Numerical examples show the effectiveness of this method.