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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Stability of Nonlinear Time-Delay Systems
Erschienen in: Stability Analysis and Robust Control of Time-Delay Systems
Verlag: Springer Berlin Heidelberg
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Since Lur’e brought up the subject of absolute stability in [
1
], three common ways of dealing with the problem of the absolute stability of Lur’e control systems have emerged. One is to use the Popov frequency-domain criterion [
2
–
5
]. The problem with it is that it is not suitable for dealing with multiple nonlinearities because it is not geometrically intuitive and cannot be examined by illustration. The second is to use the extended Popov frequency-domain criterion [
6
,
7
]. The problem here is that the condition is only sufficient. The third is a method based on a Lyapunov function in the Lur’e form [
8
,
9
]. It produces necessary and sufficient conditions for the existence of a Lyapunov function in the Lur’e form that ensures the absolute stability of a Lur’e control system with multiple nonlinearities in a bounded sector; but the conditions simply exist and are unsolvable.