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

We analyze stability and ℋ_infin 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 reasons. The aim is to find conditions concerning the controller failure time, under which the system's stability and ℋ_infin 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 the global exponential stability of the system is guaranteed. For ℋ_infin 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 a system with an ATBCF achieves a reasonable weighted ℋ_infin disturbance attenuation level, and the weighted ℋ_infin disturbance attenuation approaches normal ℋ_infin disturbance attenuation when the ATBCF is sufficiently large.