线性中立型单延迟系统李代数稳定性判据

研究了线性中立型单延迟微分系统的稳定性.从矩阵李代数可解性角度,推导出新的简单的延迟独立稳定性判据.该新判据的重要意义和优越性在于首次突破了以往大多数相关文献的稳定性判据在应用上受条件‖C‖<1,ρ(|C|)<1或ρ(|N|)<1的限制,从而首次成功确定了在‖C‖≥,ρ(|C|)≥1和ρ(|N|)≥1的情形下中立型延迟微分系统渐近稳定性.最后,通过两个例子显示了新判据的优越性.

Lie Algebraic Criteria for Stability of Linear NeutralSystems with a Single Delay

The stability of linear neutral delay-differentialsystems with a single delay is investigated. In termsof solvability of a matrix Lie algebra, new simpledelay-independent stability criteria are presented. The new criteria break through the limitation of~$\|C \|<1$,~$\rho(|C|)<1$ or ~$\rho(|N|)<1$ in the stabilitycriteria existing in the related literature and thus lead to theasymptotic stability of neutral systems with a single delay in thecase of ~$\|C \|\ge 1$,~$\rho(|C|)\ge 1$ and ~$\rho(|N|)\ge1$. Finally, two examples demonstrate the effectiveness of the newcriteria.