不确定时滞系统的时滞依赖稳定性条件研究

提出了一类时滞系统基于严格线性矩阵不等式的稳定性条件,这一条件较目前得出的稳定性条件相比具有更少的变量,使得形式上避免使用特定的增加保守性的放大不等式,但效果等价于使用了一个保守性更小的放大不等式。同时,本文还把得到的结论通过形式转换应用于研究具有凸多面体不确定性模型的时滞系统的稳定性性能。最后,用数值仿真验证了结论的有效性。

Research on Delay-Dependent Stability Criteria for Time-Delay Systems with Uncertainties

An asymptotic stability condition for time-delay systems in terms of a strict linear matrix inequality is provided in this paper, which has fewer variables compared with the stability condition presented now. Then this avoids bounding certain cross terms which often leads to conservatism but the effect is equivalent to make use of the less conservative bounding certain cross terms. Meanwhile, by transforming the proposed condition, this conclusion also is applied to the study on the stability performance of the time-delay system with polytopic uncertainty. Finally, digital simulation examples are given to illustrate the validity of the proposed method.