| 一类时间滞后关联大系统的全局指数稳定性 |
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| 引用本文： | 任殿波,张继业. 一类时间滞后关联大系统的全局指数稳定性[J]. 西南交通大学学报, 2005, 40(3): 343-346 |
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| 作者姓名： | 任殿波 张继业 |
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| 作者单位： | 西南交通大学牵引动力国家重点实验室,四川,成都,610031 |
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| 基金项目： | 国家自然科学基金资助项目（10272091）;感谢西南交通大学科学研究基金资助（X1200811070101）. |
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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．
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| 关 键 词： | M-矩阵 全局指数稳定性 大系统 向量李雅普诺夫函数 时间滞后 |
| 文章编号： | 0258-2724（2005）03-0343-04 |
| 收稿时间： | 2004-04-07 |
| 修稿时间： | 2004-04-07 |
Global Exponential Stability of a Class of Interconnected Large-Scale Systems with Time Delays |
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| REN Dian-bo,ZHANG Ji-ye. Global Exponential Stability of a Class of Interconnected Large-Scale Systems with Time Delays[J]. Journal of Southwest Jiaotong University, 2005, 40(3): 343-346 |
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| Authors: | REN Dian-bo ZHANG Ji-ye |
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| Affiliation: | National Traction Power Lab. , Southwest Jiaotong University, Chengdu 610031, China |
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| Abstract: | The global exponential stability of a class of linear interconnected large-scale systems with criterion was obtained for global exponential stability of the systems by analyzing the stability of differential inequalities with time delays under the assumption that the time delays are bounded and continuous. A large-scale system is global exponential stable if the test matrix is an M-matrix, where the test matrix is constructed by employing the coefficient matrices of the system and the solutions of the Lyapunov equations which are interconnected with the system. Since it is independent of the delays and simplifies the calculation, the criterion is easy for application. |
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| Keywords: | M-matrix global exponential stability large-scale systems vector Lyapunov function time delay |
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