广义多时滞线性定常系统ROSENBROCK方法的渐近稳定性及在控制中的应用  

Stability Analysis of Rosenbrock Methods for Generalized Multi-Delay Linear Systems and Application to Control Models

作　　者：祝乔[1] 肖爱国[2] 

机构地区：[1]湘潭大学信息工程学院,湖南湘潭411105 [2]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《湘潭大学自然科学学报》2008年第4期24-31,共8页Natural Science Journal of Xiangtan University

基　　金：国家自然科学基金资助项目(10571147);湖南省科技计划项目(2007FJ4049)

摘　　要：线性定常系统在控制理论中是基础模型,有着非常重要的地位.若考虑到系统中有多个状态产生延迟,则这类模型可描述为广义多时滞线性定常系统.该文利用Rosenbrock方法求解此类系统,并分析其渐近稳定性,证明了该方法是GPm-稳定的当且仅当它是A-稳定的.两个关于控制系统的数值例子证实了此类方法的有效性.Linear stationary systems are basic models in control theory. If we consider the systems include multi-state-delays, then the resulting models are described by a system of generalized multi-delay differential equations. In this paper, we show that the Rosenbrock methods are GPm-stable if and only if they are A- stable. Moreover, we also show the validity of Rosenbrock methods for multi-delay differential equations by computing two control models.

关 键 词：广义多时滞线性定常系统 ROSENBROCK方法 GPm-稳定性 

分 类 号：O241.8[理学—计算数学]