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Structure of finite dimensional exact estimation algebra on state dimension 3 and linear rank 2*.
- Source :
-
International Journal of Control . Feb2023, Vol. 96 Issue 2, p362-373. 12p. - Publication Year :
- 2023
-
Abstract
- The estimation algebra plays an important role in classification of finite dimensional filters. When finite dimensional estimation algebra has maximal rank, Yau et al. [Yau (2003). Complete classification of finite-dimensional estimation algebras of maximal rank. International Journal of Control, 76(7), 657–677; Yau & Hu (2005). Classification of finite-dimensional estimation algebras of maximal rank with arbitrary state-space dimension and Mitter conjecture. International Journal of Control, 78(10), 689–705.] have proved that η must be a degree 2 polynomial. In this paper, we study the structure of finite dimensional exact estimation algebra with state dimension 3 and rank 2. We establish a sufficient and necessary condition for estimation algebra with nonmaximal rank to be finite dimensional. Importantly, in the new filtering system, η needs not to be a degree 2 polynomial and can be of any degree 4 n 1 + 2 , n 1 ∈ Z + . It is the first time to systematically analyse nonmaximal rank exact estimation algebra in which η is a polynomial of any degree 4 n 1 + 2 , n 1 ∈ Z + . For Riccati-type equation, estimates have been done from the viewpoints of both classical solution and weak solution respectively. Finally, finite dimensional filters of Benés type are constructed successfully. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*FINITE, The
Subjects
Details
- Language :
- English
- ISSN :
- 00207179
- Volume :
- 96
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- International Journal of Control
- Publication Type :
- Academic Journal
- Accession number :
- 161687839
- Full Text :
- https://doi.org/10.1080/00207179.2021.1992673