The following three major aspects of the design of observers for linear time-invariant singular systems are resolved: the necessary and sufficient conditions for the problem to have a solution; the order of the minimal observer; and the properties of the closed-loop system (separation principle). An algorithm is presented for the construction of the minimal-order observer.

The preservation of the efficient functionality of a pressurized reactor unit in the presence of faults is the aim of the present paper. To satisfy this aim, a distributed supervisory control scheme, considering the possibility of system faults, was designed. Towards this aim, the models of the subsystems of the total pressurized reactor unit in the presence of sensor and actuator faults are developed, using finite deterministic automata. This is the first contribution of the paper. The desired performance of the unit was formulated in the form of rules guaranteeing the desired behavior of a pressurize–depressurize cycle and safety specifications. The rules were translated to six desired regular languages. The realization of these languages, in the form of supervisor automata, was accomplished. This is the second contribution of the paper. A modular supervisory design scheme, towards safety and tolerance in the presence of faults, was proposed and realized, and the properties of the proposed supervisors and the controlled automaton were proven. This is the third contribution of the paper. The complexity of each supervisor was computed. The efficiency of the supervisory design scheme was illustrated through simulations. A PLC implementation of the derived supervisors was proposed. The derived supervisors are suitable for implementation as function blocks.