Controller failure time analysis for symmetric 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 disturbance attenuation properties of the entire system. Our aim is to find conditions concerning controller failure time, under which the system's stability and disturbance attenuation properties are preserved to a desired level. For both stability and 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 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.