【摘要】 关于系统的状态反馈稳定性问题的研究一直是现代控制理论研究的重要问题之一.广义分布参数系统是比分布参数系统更广的一类系统,在研究复合材料热导体中的温度分布等问题时会出现这样的系统.本文讨论了H ilbert空间中一阶广义分布参数系统的状态反馈稳定性问题.应用泛函分析及线性算子半群理论的方法给出了使闭环广义分布参数系统渐进稳定的充要条件,充分条件及状态反馈的构造性表达式.这对研究广义分布参数系统的状态反馈稳定性问题具有重要的理论价值.更多还原

【Abstract】 Researches concerning the stabilization by state feedback of the system is always one of important research problems for modern control theory.Singular distributed parameter systems is a system which is broader than distributed parameter systems,it appears in the study of the temperature distribution in a composite heat conductor,etc.In this paper,stabilization by state feedback of the first order singular distributed parameter systems is discussed in Hilbert space.The necessary and sufficient conditions,sufficient conditions,and the constructive expression of the state feedback such that the closed loop singular distributed parameter system is asymptotic stability are given via functional analysis and linear operator semi-group theory.This research is theoretical important for studying the stabilization by state feedback of the singular distributed parameter systems.更多还原