时滞动力学系统的L-K稳定性条件分析  

Analysis of Lyapunov-Krasovskii Stability for Dynamical Systems with Time Delay

作　　者：张晓艳[1,3] 孙建桥 丁千[1] 

机构地区：[1]天津大学力学系,天津300073 [2]加州大学默塞得分校工学院,美国加里福尼亚默塞得95343 [3]天津电子信息职业技术学院电子系,天津300132

出　　处：《西安交通大学学报》2013年第5期72-76,共5页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(11172197)

摘　　要：针对线性时滞动力学系统的稳定性问题,比较了3种Lyapunov-Krasovskii(L-K)泛函。以一个在时滞PD反馈控制下的二阶线性系统作为数值实例,在反馈增益的参数空间中,根据不同的L-K泛函所对应的线性矩阵不等式条件计算线性系统的稳定域,并与由特征方程计算出的结果进行比较。结果表明:L-K泛函的稳定性条件是充分且保守的;Gu的完整L-K泛函的LMI不等式中暗含无穷多的矩阵,因此保守性得到很大改善,但其计算量显著增大;当将Lyapunov稳定性理论用于控制设计时,经常使用保守的稳定性条件,但Gu的L-K泛函更有利于控制器设计。Three Lyapunov-Krasovskii （L-K） functionals for stability of time-delayed linear dynamical systems are compared. A benchmark second order linear system under delayed PD feedback controls is considered. The stability domains in the feedback gain parameter space are computed from the LMIs of different L-K functionals, and are compared with that calculated from the characteristic equation of the linear system. The results show that while most L-K functionals provide sufficient conditions for stability, which are conservative, Gu＇s complete L-K functional is the least conservative and the most accurate, and provides a necessary and sufficient condition for stability. Gu＇s complete L-K functional involves implicitly infinite number of matrices, hence, with a huge computational effort. When the Lyapunov stability theory is adopted for control design, the conservative stability conditions may be used, while Gu＇s complete L-K functional is more favorable to the design of controller.

关 键 词：动力学系统 时滞 稳定性 Lyapunov—Krasovskii理论 

分 类 号：O317[理学—一般力学与力学基础]