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Controller failure time analysis for symmetric \({\mathcal H}_\infty\) control systems. (English) Zbl 1059.93040
Summary: We consider a controller failure time analysis problem for a class of symmetric linear time-invariant (LTI) systems controlled by a pre-designed symmetric static output feedback controller. We assume that the controller fails from time to time due to a physical or purposeful reason, and we analyse stability and \({\mathcal H}_\infty\) disturbance attenuation properties of the entire system. Our aim is to find conditions concerning controller failure time, under which the system’s stability and \({\mathcal H}_\infty\) disturbance attenuation properties are preserved to a desired level. For both stability and \({\mathcal H}_\infty\) disturbance attenuation analysis, we show that if the unavailability rate of the controller is smaller than a specified constant, then global exponential stability of the entire system and a reasonable \({\mathcal H}_\infty\) disturbance attenuation level is achieved. The key point is to establish a common quadratic Lyapunov-like function for the entire system in two different situations.

MSC:
93B36 \(H^\infty\)-control
90B25 Reliability, availability, maintenance, inspection in operations research
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References:
[1] Boyd SEl, SIAM (1994)
[2] Hassibi A, Proceedings of the 38th IEEE Conference on Decision and Control pp pp. 1345–1351– (1999)
[3] DOI: 10.1080/00207170210162096 · Zbl 1017.93097
[4] Ikeda M, Proceedings of the 3rd European Control Conference pp pp. 988–993– (1995)
[5] Ikeda M, Proceedings of International Conference on Control, Automation and Systems pp pp. 651–654– (2001)
[6] Iwasaki T, Taylor & Francis (1998)
[7] Khalil HK, Prentice-Hall (1996)
[8] Shimemura E, Journal of the Society of Instrument and Control Engineers 26 pp 400– (1987)
[9] DOI: 10.1016/S0167-6911(01)00125-6 · Zbl 0986.93028
[10] Zhai G, Proceedings of the 41st IEEE Conference on Decision and Control pp pp. 3869–3874– (2002)
[11] Zhai G, Proceedings of the 41st IEEE Conference on Decision and Control pp pp. 4395–4400– (2002)
[12] Zhai G, Proceedings of the 40th IEEE Conference on Decision and Control pp pp. 1029–1030– (2001)
[13] DOI: 10.1016/S0016-0032(01)00030-8 · Zbl 1022.93017
[14] Zhai G, Transactions of the Society of Instrument and Control Engineers 36 pp 1050– (2000)
[15] Zhai G, Proceedings of the 2001 European Control Conference pp pp. 138–142– (2001)
[16] DOI: 10.1109/37.898794
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