Line zonotopes: a set representation suitable for unbounded systems and its application to set-based state estimation and active fault diagnosis of descriptor systems (2401.10239v2)

Abstract: This paper proposes new methods for set-based state estimation and active fault diagnosis (AFD) of linear descriptor systems (LDS). In contrast to intervals, ellipsoids, and zonotopes, linear static constraints on the state variables, typical of descriptor systems, can be directly incorporated in the mathematical description of constrained zonotopes (CZs). Thanks to this feature, methods using CZs could provide less conservative enclosures than zonotope methods. However, an enclosure on the states should be known for all $k \geq 0$, which is not true in the case of unstable or unobservable LDS. In this context, this paper proposes a new representation for unbounded sets, which allows to develop methods for state estimation and AFD of stable and unstable LDS. Unlike many other extensions of CZs, the proposed set inherits most of their properties, including polynomial time complexity reduction methods, while allowing to describe different classes of sets, such as strips, hyperplanes, and the entire $n$-dimensional Euclidean space. The advantages of the proposed approaches with respect to CZ methods are highlighted in numerical examples.