Controller failure time analysis for symmetric ℋ_∞ control systems

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 controller. We assume that the controller fails from time to time due to a physical or purposeful reason, and we analyse stability and ℋ_∞ disturbance attenuation properties of the entire system. Our aim is to find conditions concerning controller failure time, under which the system's stability and ℋ_∞ disturbance attenuation properties are preserved to a desired level. For both stability and ℋ_∞ 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 ℋ_∞ 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.