【摘要】 研究了具有离散时滞和分布时滞的一类混合时滞广义系统容许性条件.首先,针对具有混合时滞的广义系统构造了一类新型的增广Lyapunov-Krasovskii泛函,加入了三重积分项.然后,对Lyapunov-Krasovskii泛函求导后产生的积分项,应用边界估值更为精确的Bessel-Legendre不等式进行处理.利用李雅普诺夫第二方法,以线性矩阵不等式的形式给出具有混合时滞的广义系统容许性条件.最后,利用数值算例借助MATLAB中LMI工具箱求解,验证了所用方法的可行性和有效性.更多还原

【Abstract】 The admissibility condition for singular systems with a class of mixed time delays consisting of discrete and distributed delays is investigated. Firstly, a novel class of augmented Lyapunov-Krasovskii functional is constructed for singular systems with mixed time delays, and a triple integral term is added. Then, the Bessel-Legendre inequality, which is more accurate in boundary estimation, is applied to deal with the integral term generated of Lyapunov-Krasovskii functional produced by derivations. An admissibility condition of singular systems with mixed delays is given by virtue of linear matrix inequality by Lyapunov’s second method. Finally, the numerical examples solving with LMI toolbox in MATLAB are provided to demonstrate feasibility and validity of the proposed method.更多还原