一类奇异摄动时滞不确定系统鲁棒稳定性

Robust Stability of a Kind of Singularly Perturbed Systems with Time-delay

为了解决复杂工业过程控制系统由于工程设计时模型描述的不完全性造成的不稳定,针对一类常见的奇异摄动时滞不确定线性系统,研究了其鲁棒稳定性问题。通过对系统各参数H∞范数有界摄动分析,获得了系统时滞有关稳定的充分条件。给出了保证系统稳定的时滞τ及奇异摄动参数ε的上界,在工程设计中为复杂工业过程控制系统稳定边界的判别提供了简单有效的手段。应用实例表明了奇异摄动时滞不确定系统鲁棒稳定性充分条件使用的方便性。

To the unstability of complex industry process control systems caused by model design, robust stability problems are discussed for singularly perturbed uncertain linear systems with time-delay. Sufficient conditions of delay-dependent stability are derived by discussing the systems with parameters perturbation bounded by H~ -norm, The upper bounds of singular perturbation parameter and time-delay are given, It is a powerful way to find out the stability bounds of complex industry process control systems in engineering design. An illustrative example shows the convenience of the methods.