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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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\textit{G. Zhai} and \textit{H. Lin}, Int. J. Control 77, No. 6, 598--605 (2004; Zbl 1059.93040)

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