Fault isolation filter with linear matrix inequality solution to optimal decoupling

In this paper we consider a model-based fault detection and isolation problem for linear time-invariant dynamic systems subject to faults and disturbances. We use an observer scheme that cancels the system dynamics and defines a residual vector signal that is sensitive only to faults and disturbances. We then design a stable fault isolation filter such that the H_infin-norm of the transfer matrix function from disturbances to the residual is minimized (for fault detection) subject to the constraint that the transfer matrix function from faults to residual is equal to a pre-assigned diagonal transfer matrix (for fault isolation). The optimization of disturbance decoupling is accomplished via the help of linear matrix inequalities. A numerical example is also presented to illustrate the algorithm