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A general theory for matrix root-clustering in subregions of the complex plane
Abstract
We consider the general problem of root-clustering of a matrix in the complex plane: LetA \in C^{n \times n}andS \subset C. Find the largest class ofSand an algebraic criterion which is necessary and sufficient for\lambda_{i}[A] \in S, i=1,2,..., n. We introduce two types of regions which constitute the largest class ofSknown to date. The criterion is presented both for open regions and closed ones. The results are used to define a design methodology for control systems. Moreover, all classical results are shown to be special cases of the present theory.
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Cites
Linear Multivariable Control: a Geometric Approach
Wonham, W. M. (1979) · Springer eBooks · doi:10.1007/978-1-4684-0068-7 · Cited by 2,997
Observers for multivariable systems
Luenberger, D. (1966) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1966.1098323 · Cited by 1,763
Dynamics of Atmospheric Flight
Etkin, B. (1972) · Defense Technical Information Center (DTIC) · Cited by 1,506
A Survey of Matrix Theory and Matrix Inequalities.
Bellman, R., Marcus, M., & Minc, H. (1965) · The American Mathematical Monthly · doi:10.2307/2315999 · Cited by 842
Introduction to Matrix Analysis
Gillies, A. W. (1960) · Physics Bulletin · doi:10.1088/0031-9112/11/7/011 · Cited by 597
Pole placement using dynamic compensators
Brasch, F., & Pearson, J. (1970) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1970.1099352 · Cited by 361
Cited by
Controller design with regional pole constraints
Haddad, W. M., & Bernstein, D. S. (1992) · IEEE Transactions on Automatic Control · doi:10.1109/9.109638 · Cited by 256
Metadata
- Authors
- Gutman, S., & Jury, E.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 1981-08
- Volume
- 26
- Issue
- 4
- Pages
- 853-863
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W1972848510
- Cited by
- 269
- References
- 6
- FWCI
- 15.29
- Type
- journal article
- Language
- en
- Open access
- closed
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