On the maximum feedback delay in a linear/nonlinear control system with input disturbances caused by controller-computer failures

Electromagnetic interferences or other environmental disturbances may cause transient failures to the controller computer of a real-time control system. Such a faulty controller either fails to update the control input for one or more sampling periods, or generates erroneous control inputs until the failure is handled properly or disappears. The goal of this paper is to derive the maximum duration of controller´s faulty behavior, called the hard deadline, a real-time control system can tolerate without losing stability or leaving its allowed state space. For linear time-invariant control systems, one can derive hard deadlines by testing the stability of their state difference equations which account for the effects of stationary occurrences of disturbances to, as well as the random delays in, the control input. Similarly, one can derive deadlines for nonlinear time-invariant control systems by linearizing their nonlinear state equations and using the Lyapunov´s first method. In addition to this stationary model, a one-shot event model is considered for linear/nonlinear time-invariant control systems by using their state trajectories and allowed state spaces. The hard deadline information that represents the knowledge of the controlled process´s inertia and timing constraints is applied to the design and evaluation of controller computers