Design of H∞ detection filter with variance constraints and arbitrarily assigned eigenvalues

Fault detection filters are a special class of observers that can generate directional residuals for the purpose of fault isolation. This paper proposes a new approach to design H_∞ fault detection filters with variance constraints in which the eigenvalues can be arbitrarily assigned, so that the residual vector, generated by this filter, has directional properties. This is done by combining the H_∞ filter and fault detection filter principles. The paper proposes a H_∞ fault detection filter and gives necessary and sufficient conditions for its existence. After the H_∞ norm and the variance constraints are satisfied, the remaining design freedom can be used to make the residual have the directional property, based on the fault detection filter principle. An illustrative example is given to show the applicability of the proposed approach.