Conditions for Robustness and Nonrobustness of theStability of Feedback Systems with Respect to Small Delays inthe Feedback Loop
Conditions for Robustness and Nonrobustness of theStability of Feedback Systems with Respect to Small Delays inthe Feedback Loop
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DOI：
10.1137/s0363012993250700
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发表时间：
1996-03
影响因子：
2.2
通讯作者：
H. Logemann;R. Rebarber;G. Weiss
中科院分区：
文献类型：
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作者：
H. Logemann;R. Rebarber;G. Weiss
人们已经观察到，对于许多稳定的反馈控制系统，在回路中引入任意小的时间延迟都会导致不稳定。在本文中，我们对分布参数系统的这一现象进行了系统的频域处理。我们考虑所有在某个右半平面有界且沿实轴在正无穷处有极限的矩阵值传递函数类。这类传递函数被称为正则的。在正则传递函数通过单位输出反馈稳定的假设下，我们给出了回路中关于小时间延迟的稳定性的鲁棒性和非鲁棒性的充分条件。这些条件是根据开环系统的高频特性给出的。此外，我们讨论了具有动态补偿器的反馈系统关于小延迟的稳定性鲁棒性。特别地，我们表明，如果一个在闭右半平面有无穷多个极点的对象被一个控制器稳定，那么其稳定性关于延迟是不鲁棒的。我们表明由小延迟产生的不稳定性本身对小延迟是鲁棒的。给出了三个例子来说明这些结果。
It has been observed that for many stable feedback control systems, the introduction of arbitrarily small time delays into the loop causes instability. In this paper we present a systematic frequency domain treatment of this phenomenon for distributed parameter systems. We consider the class of all matrix-valued transfer functions which are bounded on some right half-plane and which have a limit at $+\spinfty$ along the real axis. Such transfer functions are called regular. Under the assumption that a regular transfer function is stabilized by unity output feedback, we give sufficient conditions for the robustness and for the nonrobustness of the stability with respect to small time delays in the loop. These conditions are given in terms of the high-frequency behavior of the open-loop system. Moreover, we discuss robustness of stability with respect to small delays for feedback systems with dynamic compensators. In particular, we show that if a plant with infinitely many poles in the closed right half-plane is stabilized by a controller, then the stability is not robust with respect to delays. We show that the instability created by small delays is itself robust to small delays. Three examples are given to illustrate these results.