The converging-input converging-state property for Lur’e systems

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• 作者：Adam Bill ; Chris Guiver ; Hartmut Logemann…
• 关键词：Absolute stability ; Circle criterion ; Converging ; input converging ; state property ; Input ; to ; state stability ; Lur’e systems ; Non ; negative systems
• 刊名：Mathematics of Control, Signals, and Systems
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：29
• 期：1
• 全文大小：1024KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory, Control; Control, Robotics, Mechatronics; Communications Engineering, Networks;
• 出版者：Springer London
• ISSN：1435-568X
• 卷排序：29

文摘

Using methods from classical absolute stability theory, combined with recent results on input-to-state stability (ISS) of Lur’e systems, we derive necessary and sufficient conditions for a class of Lur’e systems to have the converging-input converging-state (CICS) property. In particular, we provide sufficient conditions for CICS which are reminiscent of the complex Aizerman conjecture and the circle criterion and connections are also made with small gain ISS theorems. The penultimate section of the paper is devoted to non-negative Lur’e systems which arise naturally in, for example, ecological and biochemical applications: the main result in this context is a sufficient criterion for a so-called “quasi CICS” property for Lur’e systems which, when uncontrolled, admit two equilibria. The theory is illustrated with numerous examples.