Annihilator design for linear parameter varying systems

Computation of the annihilator of a linear parameter-dependent (LPV) dynamical system is an important subtask in several fields of control theory, such as fault detection design or reconfigurable control design. While for LTI systems the problem can be efficiently handled, for LPV systems is not available a single algorithm that would provide the desired annihilator. Thus alternative solutions are needed to handle the cases that might appear in applications. This paper provides new insights and additional technical details for the authors’ previously proposed inversion based technique. As an alternative, for a special class of LPV systems where the parameter variation is affine, this paper provides an extension of the LTI techniques that computes the annihilator based on the geometric framework. A comparison of the two approaches gives an opportunity to illustrate some of the intricacies of the LPV modeling.