On computing least order fault detectors using rational nullspace bases

Abstract

We propose a numerically reliable computational approach to design least order fault detectors using descriptor system techniques. This approach is based on a new numerically stable algorithm to compute least order rational nullspace bases of rational matrices. The main computation in this algorithm is the orthogonal reduction of the system pencil matrix to a Kronecker-like form. The proposed approach can be combined with coprime factorization techniques to determine stable rational bases. Least order fault detectors can be determined by selecting an appropriate linear combination of basis vectors by eliminating non-essential dynamics. The proposed approach is applicable to both standard and descriptor system descriptions.