Derivation of Hard Deadlines for Real-Time Control Systems

The computation-time delay in the feedback controller of a real-time control system may cause failure to update the control input during one or more sampling periods. A dynamic failure is said to occur if this delay exceeds a certain limit called a hard deadline. We present a method for calculating the hard deadlines in linear time-invariant control systems. To derive necessary conditions for (asymptotic) system stability, the state difference equation is modified based on an assumed maximum delay and the probability distribution of delays whose magnitudes are less than, or equal to, the assumed maximum delay. Moreover, the allowed state-space - which is derived from given input and state constraints - is used to calculate the hard deadline as a function of time and the system state. We also consider a one-shot delay model in which a single event causes a dynamic failure.