New computational approach for the design of fault detection and isolation filters

Abstract

We propose a numerically reliable computational approach for the design of residual generators for fault detection and isolation filters. The new approach is based on computing solutions of least dynamical orders of linear equations with rational matrix coefficients in combination with special rational factorizations. The main computational ingredients are the orthogonal reduction of the associated system matrix pencil to a certain Kronecker-like staircase form, the solution of a minimal dynamic cover design problem, and the computation of stable and proper rational factorizations with diagonal denominators. For all these computations we discuss numerically reliable algorithms relying on matrix pencil and descriptor system techniques. The proposed residual generator design approach is completely general, is applicable to both continuous- and discrete-time systems, and can easily handle even unstable and/or improper systems.