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Mathematical Description of Linear Dynamical Systems
Abstract
There are two different ways of describing uynamicu systems: (i) bymeans of state variables and (ii) by input/output relations. The first method may be regarded as an axiornatization of Newton’s laws of mechanics and is taken to be the basic definition of a system. It is then shown (in the linear case) that the input/output relations determine only one part of a system, that which is completely observable and completely controllable. Using the theory of controllability and observability, methods are given for calculating irreducible realization of a given impulse-response matrix. In particular, an explicit procedure is given to determine the minimal number of state variables necessary to realize a given transfer-function matrix. Difficulties arising from the use of reducible realizations are discussed briefly.
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Cited by
An eigensystem realization algorithm for modal parameter identification and model reduction
Juang, J.-N., & Pappa, R. S. (1985) · Journal of Guidance, Control, and Dynamics · doi:10.2514/3.20031 · Cited by 2,762
Observers for multivariable systems
Luenberger, D. (1966) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1966.1098323 · Cited by 1,763
Bellman, R., & Åström, K. J. (1970) · Mathematical Biosciences · doi:10.1016/0025-5564(70)90132-x · Cited by 871
Numerical Identification of Linear Dynamic Systems from Normal Operating Records
Åström, K.-J., & Torsten, B. (1965) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)69024-4 · Cited by 272
Optimally controlling the human connectome: the role of network topology
Betzel, R. F., Gu, S., Medaglia, J. D., Pasqualetti, F., & Bassett, D. S. (2016) · Scientific Reports · doi:10.1038/srep30770 · Cited by 247
Metadata
- Authors
- Kalman, R. E.
- Venue
- Journal of the Society for Industrial and Applied Mathematics Series A Control
- Published
- 1963-01
- Volume
- 1
- Issue
- 2
- Pages
- 152-192
- ISSN
- 0036-1402 (ISSN-L)
- 0887-4603
- OpenAlex
- W1994368767
- Cited by
- 1,738
- References
- 0
- FWCI
- 67.64
- Type
- journal article
- Language
- en
- Open access
- closed
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