具有变时滞的线性系统的时滞相关稳定性

摘要

The control system with delay is an important nonlinear controlsystem in engineering. In this paper, the problem of the robust stability and decay estimations of such control system is considered. Several new criteria are given by applying the differential theorem, the decay rate for this class of system is also obtained. The only assumption is that the delay is bounded, the results here can be applied to the systems with varying time delay. Finally, a numerical computation is presented for illustration and comparison with previous results, which shows that the method is effective.%具有时滞的控制系统是工程实践中经常遇到的一类重要的非线性控制系统。根据微分方程理论和矩阵指数特性，提出了具有不确定性的时滞控制系统与时滞相关和与时滞无关稳定的充分性判据，并给出系统衰减速率的估计方法。该方法仅需假定时滞有界，因而其结论适用于变时滞的系统。同时还给出了应用实例，并与相关成果进行了比较，计算结果表明了该方法的有效性。