Disturbance rejection problem solvability: From structural approach to reliability/availability analysis

The aim of the paper is to study the impact of component failures on an important control problem for an automated system when operating: the disturbance rejection. The paper proposes a method based on a graph–theoretical approach to study the reliability and the availability of the controller capacity to reject some external disturbances. Only the system structure is considered known. The paper focuses on external and internal component failures and assumes that their probabilities are known. The satisfaction conditions of the disturbance rejection problem solvability for the structured linear systems are recalled. The first contribution of the paper is to express this property as a Boolean expression based on the functioning state of the involved component. A second contribution is to extend the definition of the reliability and the availability to cover the disturbance rejection ability and to assess the probability to conserve or to lose this property according to the components reliability and availability.