一类时间滞后关联大系统的全局指数稳定性
G lobalExponential Stability of a C lass of Interconnected Large-Scale System swith Time Delays
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摘要: 利用M-矩阵理论,通过构造适当的向量李雅普诺夫函数,研究一类具有时变时间滞后的线性关联大系 统的全局指数稳定性.在时间滞后连续且有界的条件下,通过分析具有时间滞后的微分不等式的稳定性,得到了 该类大系统全局指数稳定的一个判据.该判据利用大系统的系数矩阵以及与大系统关联的李雅普诺夫矩阵方程 的解构造判定矩阵,根据判定矩阵是否为M-矩阵判定大系统的全局指数稳定性.该判据计算简便,且与时间滞 后量无关,便于应用.Abstract: The global exponential stability of a class of linear interconnected large-scale systemswith time delayswas analyzed based onM-matrix theory and by constructing a vectorLyapunov function. A criterion was obtained for global exponential stability of the systems by analyzing the stability of differential inequalitieswith time delays under the assumption that the time delays are bounded and continuous. A large-scale system is global exponential stable if the testmatrix is anM-matrix, where the testmatrix is constructed by employing the coefficientmatricesof the system and the solutionsof the Lyapunov equationswhich are interconnectedwith the system. Since it is independentof the delays and simplifies the calculation, the criterion is easy for application.
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Key words:
- M-matrix /
- global exponential stability /
- large-scale systems /
- vector Lyapunov function /
- time delay
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