Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, December 9-12, 2003.

Abstract -- In this paper, 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. We assume that the controller fails from time to time due to physical or purposeful reason, and analyze stability and H1 disturbance attenuation properties for the entire system. Our objective is to find conditions concerning controller failure time, under which the system’s stability and H1 disturbance attenuation properties are preserved to a desired level. For both stability and H1 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 H1 disturbance attenuation level is achieved. The key point is to establish a common quadratic Lyapunov-like function for the case where the controller works and the case where the controller fails.

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