Lur'e Lyapunov functions and absolute stability criteria for Lur'e systems with multiple nonlinearities |
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| Authors: | Chunyu Yang Qingling Zhang Linna Zhou |
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| Affiliation: | 1. Institute of Systems Science, Northeastern University, Shenyang, Liaoning Province 110004, People's Republic of China;2. Institute of Systems Science, Northeastern University, Shenyang, Liaoning Province 110004, People's Republic of ChinaInstitute of Systems Science, Northeastern University, Shenyang, Liaoning Province 110004, People's Republic of China=== |
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| Abstract: | In this paper, the absolute stability problem of Lur'e systems with multiple nonlinearities is investigated. Popov‐type absolute stability criteria are surveyed and classified by distinguishing the Lur'e Lyapunov function upon which the criteria are based. A modified Lur'e Lyapunov function is presented. Some necessary and sufficient conditions for the existence of the Lyapynov function to guarantee the absolute stability of Lur'e systems are derived. By these conditions, LMI‐based stability criteria are presented. The obtained criteria are expected to be less conservative than the existing ones. Finally, numerical examples are given to illustrate the advantages and effectiveness of our results. Copyright © 2006 John Wiley & Sons, Ltd. |
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| Keywords: | Lur'e systems absolute stability Lur'e Lyapunov function linear matrix inequality (LMI) |
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