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By using generalized Riccati equations, a method of designing observer-based feedback controllers against sensor failures for detectable descriptor linear systems is presented. A parameterization of the observer-based fault-tolerant feedback controllers is provided. The controller designed by the proposed method guarantees that the closed-loop system is regular, impulse-free and stable in the normal condition as well as in the event of sensor failures. A numerical example shows the effect of the proposed method.