Derivation and application of hard deadlines for real-time control systems

A method for calculating the hard deadlines in linear time-invariant control systems by considering system stability and the allowed state-space is presented. 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. 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. A one-shot delay model in which a single event causes a dynamic failure is considered. The knowledge of hard deadline is applied to the design of error recovery in a triple modular redundant controller computer