Ellipsoidal set-membership state estimation for descriptor systems

Abstract

This paper presents an ellipsoidal set-membership state estimation technique for discrete-time linear time-invariant descriptor systems with bounded perturbations and noises. The approach proceeds off-line by minimizing a parameter with respect to a linear matrix inequality (LMI). The system state of the considered descriptor system is guaranteed to belong to an ellipsoidal set at each time instant. Finally, the proposed technique is analyzed via an illustrative example.

Tight interval state estimate for discrete‐time descriptor linear systems

“…However, few research works in the literature related to set‐membership state estimation approaches can be found for this type of systems. For example, in References 32,33, ellipsoidal set‐membership state estimations have been developed for descriptor systems with bounded perturbations and noises. Interval analysis is also used in the works 34,35 to synthesize an interval state estimator.…”

Zonotopic fault detection observer for discrete-time descriptor systems considering − fault sensitivity

“…Different types of sets have been considered in the literature, such as ellipsoids and zonotopes. Some works related to ellipsoidal set-membership approaches can be found in (Chabane et al, 2014;Merhy et al, 2019). Alternatively, zonotopes, known as one of symmetric sets, have simple computational load based on operations involving centre and matrix.…”

Set-based state estimation and fault diagnosis of linear discrete-time descriptor systems using constrained zonotopes

“…Set-based strategies for state estimation of discrete-time descriptor systems with unknown-but-bounded uncertainties is a recent subject, often addressed using intervals, zonotopes and ellipsoids (Efimov et al, 2015;Wang et al, 2018a,b;Merhy et al, 2019). Interval methods are used in Efimov et al (2015) to design a state estimator for time-delay descriptor systems based on linear matrix inequalities and the Luenberger structure.…”

“…These strategies are extended in Wang et al (2018b) for linear parametervarying descriptor systems, but conservative enclosures are still present since the intersection method is maintained. Ellipsoids are used in Merhy et al (2019) for state estimation of linear descriptor systems based on Luenberger type observers. Despite being able to provide stable bounds, the ellipsoidal estimation can be conservative since the complexity of the set is fixed and static relations are not directly incorporated.…”

“…In particular, the former relies on the solution of linear matrix inequalities, while the latter requires the solution of a Sylvester equation. Luenberger-type observers have been also used in Merhy et al (2019) for state estimation of LDS, but with sets described by ellipsoids. Despite being able to provide stable bounds, intervals and ellipsoids are conservative since the complexity of the sets is fixed, leading to significant wrapping effect.…”