Detection filter design for LPV systems -- a geometric approach.
Consider the linear parameter varying (LPV) system \(\dot{x}(t) = A(\rho) x(t) + B(\rho) u(t) + L_1(\rho)m_1(t) + L_2(\rho) m_2(t)\), with measurement \(y(t) = C x(t)\). As the name suggests the parameters appear linearly, e.g., \(A(\rho) = \sum_{j=0}^N \rho_j A_j\). It is further assumed that the parameters and their derivatives are bounded signals. The signals \(m_1, m_2\) model possible faults. The aim of the paper is to design a fault detection filter, i.e., a second system which indicates which fault has occurred. The authors solve this problem by using the geometric theory. Their main result states that if the smallest unobservable subspace containing \({\mathcal L}_2\) has zero intersection with \({\mathcal L}_1\), then this problem is solvable. Here \({\mathcal L}_i =\sum_{j=0}^N\)\,Im \(L_{i,j}\). If the parameters \(\rho_j\) are differentially independent, then this condition is also necessary. Furthermore, they give the formula for the filter and present a condition implying stability. The results are applied to the model of a small aircraft.
scientific article; zbMATH DE number 2056281