Detection filter design: Spectral theory and algorithms

A new formulation of the detection filter problem is generated by assignment of the closed-loop eigenstructure under certain constraints. Detection filters, which are actually a specific class of observers, fix the output error direction of the system so that it can be associated with a particular failure mode and its known design failure direction. The derivation of detection filters from an eigensystem assignment approach permits a very transparent theory. The detection filter gains and closed-loop eigenvectors are obtained from a set of simultaneous equations. Necessary and sufficient conditions for the solution of these algebraic equations are determined which produce a complete theory for detection filters.