Analysis of Lyapunov-Krasovskii stability for dynamical systems with time delay

被引：0
作者：
Zhang, Xiaoyan [1 ,3 ]
Sun, Jianqiao [2 ]
Ding, Qian [1 ]
机构：
[1] Department of Mechanics, Tianjin University
[2] School of Engineering, University of California, Merced
[3] Department of Electronics, Tianjin Electronic Information Vocational Technology College
来源：
Hsi-An Chiao Tung Ta Hsueh/Journal of Xi'an Jiaotong University | 2013年 / 47卷 / 05期
关键词：
Dynamical system; Lyapunov-Krasovskii theory; Stability; Time delay;
D O I：
10.7652/xjtuxb201305013
中图分类号：
学科分类号：
摘要：
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.
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页码：72 / 76
页数：4
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