The eigenstructure assignment method has been used, to conduct linear-matrix-inequality-based robust fault detection and isolation in physical systems. The eigenstructure assignment method is realized by the concept of detection spaces in physical systems. The linear matrix inequality (LMI) technique can be used to find optimal filter, reducing the noise effect on the residual, after a set of stable eigenvalues is assigned to each independent detection space. The LMI technique is also used to solve the optimal filter problem that is computationally efficient. The LMI technique is also used to design a robust detection filter that can detect and isolate disturbances in systems.