The Linear Multivariable Regulator Problem
Abstract
The problem is considered of regulating in the face of parameter uncertainty the output of a linear time-invariant system subjected to disturbance and reference signals. This problem has been solved by other researchers. In this paper a new and simpler algebraic solution is given.
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Early lumping approximates the infinite-dimensional system with a finite-dimensional model.
“One is early lumping, which approximates the infinitedimensional system with a finite-dimensional model.[2,3]”
From Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport <scp>PDEs</scp> (2025) · cites this paper as [3]
Cites
The internal model principle for linear multivariable regulators
Francis, B. A., & Wonham, W. M. (1975) · Applied Mathematics & Optimization · doi:10.1007/bf01447855 · Cited by 1,063 · see citing works
Self-citationAccomodation of external disturbances in linear regulator and servomechanism problems
Johnson, C. D. (1971) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1971.1099830 · Cited by 608 · see citing works
Robust control of a general servomechanism problem: The servo compensator
Davison, E. J., & Goldenberg, A. A. (1975) · Automatica · doi:10.1016/0005-1098(75)90022-9 · Cited by 403 · see citing works
An approach to the linear multivariable servomechanism problem†
Young, P. C., & Willems, J. C. (1972) · International Journal of Control · doi:10.1080/00207177208932211 · Cited by 267 · see citing works
Optimal control of the linear regulator with constant disturbances
Johnson, C. D. (1968) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1968.1098947 · Cited by 262 · see citing works
Davison, E. (1972) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1972.1100084 · Cited by 225 · see citing works
Design of industrial regulators. Integral feedback and feedforward control
Smith, H. W., & Davison, E. J. (1972) · Proceedings of the Institution of Electrical Engineers · doi:10.1049/piee.1972.0233 · Cited by 152 · see citing works
Regulation and Internal Stabilization in Linear Multivariable Systems
Wonham, W. M., & Pearson, J. B. (1974) · SIAM Journal on Control · doi:10.1137/0312002 · Cited by 98 · see citing works
Design of minimal order stable observers for linear functions of the state via realization theory
Roman, J. J. P., & Bullock, T. E. (1975) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1975.1101061 · Cited by 74 · see citing works
Control of Linear Systems through Specified Input Channels
Corfmat, J., & Morse, A. (1976) · SIAM Journal on Control and Optimization · doi:10.1137/0314014 · Cited by 70 · see citing works
Minimal order observers for estimating linear functions of a state vector
Moore, J. B., & Ledwich, G. F. (1975) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1975.1101054 · Cited by 68 · see citing works
The feedforward control of linear multivariable time-invariant systems
Davison, E. J. (1973) · Automatica · doi:10.1016/0005-1098(73)90042-3 · Cited by 64 · see citing works
On error systems and the servomechanism problem†
Bhattacharyya, S. P., & Pearson, J. B. (1972) · International Journal of Control · doi:10.1080/00207177208932219 · Cited by 50 · see citing works
Robust solutions to linear multivariable control problems
Pearson, J. P., Shields, R., & Staats, P. W. (1974) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1974.1100679 · Cited by 42 · see citing works
On zeroing the output of a linear system
Bhattacharyya, S. P., Pearson, J. B., & Wonham, W. M. (1972) · Information and Control · doi:10.1016/s0019-9958(72)90321-x · Cited by 39 · see citing works
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Moadeli, B., Cassol, G. O., & Dubljevic, S. (2025) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.25629 · Cited by 4 · see citing works
- Authors
- Francis, B. A.
- Corresponding author
- Francis, Bruce A.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 1977-05
- Volume
- 15
- Issue
- 3
- Pages
- 486-505
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W2118589723
- Cited by
- 1,092
- References
- 15
- Citations by year
- 2026: 22 · 2025: 27 · 2024: 36 · 2023: 35 · 2022: 31 · 2021: 25 · 2020: 24 · 2019: 49 · 2018: 51 · 2017: 52 · 2016: 52 · 2015: 43 · 2014: 45 · 2013: 33 · 2012: 39
- FWCI
- 5.58
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- SIAM Journal on Control and Optimization (publishedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Design
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
- Keywords
- parameter uncertainty, linear time-invariant systems, disturbance rejection, reference tracking, algebraic solutions, output regulation
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