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Observing the State of a Linear System
Abstract
In much of modern control theory designs are based on the assumption that the state vector of the system to be controlled is available for measurement. In many practical situations only a few output quantities are available. Application of theories which assume that the state vector is known is severely limited in these cases. In this paper it is shown that the state vector of a linear system can be reconstructed from observations of the system inputs and outputs. It is shown that the observer, which reconstructs the state vector, is itself a linear system whose complexity decreases as the number of output quantities available increases. The observer may be incorporated in the control of a system which does not have its state vector available for measurement. The observer supplies the state vector, but at the expense of adding poles to the over-all system.
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Citations
Cites
A New Approach to Linear Filtering and Prediction Problems
Kalman, R. E. (1960) · Journal of Basic Engineering · doi:10.1115/1.3662552 · Cited by 31,751
Cited by
Luenberger, D. (1971) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1971.1099826 · Cited by 2,709
Self-citationObservers for multivariable systems
Luenberger, D. (1966) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1966.1098323 · Cited by 1,763
Self-citationReview and classification of recent observers applied in chemical process systems
Mohd Ali, J., Ha Hoang, N., Hussain, M. A., & Dochain, D. (2015) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2015.01.019 · Cited by 239
Research and Development of Electro-hydraulic Control Valves Oriented to Industry 4.0: A Review
Xu, B., Shen, J., Liu, S., Su, Q., & Zhang, J. (2020) · Chinese Journal of Mechanical Engineering · doi:10.1186/s10033-020-00446-2 · Cited by 193
Nguyen, M. H., Dao, H. V., & Ahn, K. K. (2023) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.6421 · Cited by 48
Metadata
- Authors
- Luenberger, D. G.
- Venue
- IEEE Transactions on Military Electronics
- Published
- 1964
- Volume
- 8
- Issue
- 2
- Pages
- 74-80
- ISSN
- 0536-1559 (ISSN-L)
- OpenAlex
- W2097089521
- Cited by
- 1,698
- References
- 1
- FWCI
- 2.98
- Type
- journal article
- Language
- en
- Open access
- closed
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- Luenberger, D. G. (1964). Observing the State of a Linear System. IEEE Transactions on Military Electronics. https://doi.org/10.1109/tme.1964.4323124
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