Detection of the appearance of new eigenvalues in dynamic systems

The geometric approach is used to describe the modeling issues associated with the increase of the number of eigenvalues of a state representation (i.e., increase of the state dimension) and the design of a detection filter. Detection filters are particular classes of observers or filters generating residuals with directional characteristics that can be associated with some a priori known changes or failure modes of the system. The detection filter approach is applied to the derivation of failure signatures and conditions of output separability and mutual detectability used for the filter design. It is assumed that the state space model describing the system´s dynamics is known and that the failure modes can be described by known additive terms in the state or observational equations. These failure models are appropriate to describe actuator and sensor failures, but failure models describing changes in the eigenstructure of the system can also be elaborated