Stability and H_∞ disturbance attenuation analysis for LTI control systems with controller failures

In this paper, we analyze stability and H_∞ disturbance attenuation properties for linear time-invariant (LTI) systems controlled by a pre-designed dynamical output feedback controller which fails from time to time due to physical or purposeful reason. 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 stability, by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant and the average time interval between controller failures (ATBCF) is large enough, then global exponential stability of the system is guaranteed. For H_∞ disturbance attenuation, also by using a piecewise Lyapunov function, we show that if the unavailability rate of the controller is smaller than a specified constant, then the system with an ATBCF achieves a reasonable weighted H_∞ disturbance attenuation level, and the weighted H_∞ disturbance attenuation approaches normal H_∞ disturbance attenuation when the ATBCF is sufficiently large.