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International Journal of Control Volume 43, 1986 - Issue 2
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Original Articles

Optimal H∞ robustness and the relationship to LQG design problems

M. J. GRIMBLE lndustrial Control Unit, Department of Electronic and Electrical Engineering, Royal College Building, University of Strathclyde, 204 George Street, Glasgow, Gl 1XW
Pages 351-372 | Received 06 Jun 1985, Published online: 27 Mar 2007

Citations (76)

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Mike J. Grimble. (2012) Factorised H ∞ control of nonlinear systems. International Journal of Control 85:7, pages 964-982.
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E. Alfaro-Cid, E.W. McGookin & D.J. Murray-Smith. (2008) Optimisation of the weighting functions of an ∞ controller using genetic algorithms and structured genetic algorithms. International Journal of Systems Science 39:4, pages 335-347.
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M. J. Grimble. (2004) Robustness of full-order and restricted-structure optimal control systems. International Journal of Systems Science 35:6, pages 375-388.
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Vijay V Patel & K B Datta. (1997) H∞-Robust Optimal Controller with Integral Action for a Coupled Tank System. IETE Journal of Research 43:1, pages 11-22.
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A. CASAVOLA, D. FRAGOPOULOS & M. J. GRIMBLE. (1996) A polynomial solution to the scalar 4-block H ∞ general distance problem. International Journal of Control 65:1, pages 33-52.
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M. J. GRIMBLE. (1995) H/ H∞ robust control design for a generalized control structure and flight control application. International Journal of Systems Science 26:11, pages 2043-2068.
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ALESSANDRO CASAVOLA. (1995) A polynomial solution to the generalized H∞ control problem with measurement noise. International Journal of Control 61:2, pages 443-458.
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KEITHG. WOODGATE. (1994) Note on the generalized H∞-optimal control problem. International Journal of Control 60:1, pages 153-156.
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ALESSANDRO CASAVOLA. (1993) Three-degree-of-freedom joint H2/H∞ optima) controllers. International Journal of Systems Science 24:9, pages 1803-1813.
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M. O. NAWARI. (1991) Multivariable closed-loop poles allocation and minimal sensitivity: a synthesis approach. International Journal of Systems Science 22:2, pages 261-271.
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G. P. LlU. (1990) Frequency-domain approach for critical systems. International Journal of Control 52:6, pages 1507-1519.
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N. A. FAIRBAIRN & M. J. GRIMBLE. (1990) H∞ robust controller for self-tuning applications Part 3. Self-tuning controller implementation. International Journal of Control 52:1, pages 15-36.
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M. J. GRIMBLE. (1989) Extensions to H∞ multivariable robust controllers and the relationship to LQG design problems. International Journal of Control 50:1, pages 309-338.
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M. J. GRIMBLE. (1988) State-space approach to H∞optimal control. International Journal of Systems Science 19:8, pages 1451-1468.
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M. J. GRIMBLE. (1987) Simplification of the equations in the paper ‘Optimal H∞ robustness and the relationship to LQG design problems’. International Journal of Control 46:5, pages 1841-1843.
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A. P. ROBERTS. (1987) Stochastic regulator with dynamic cost weighting. International Journal of Control 45:3, pages 1103-1111.
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Articles from other publishers (60)

T. J. Moir. (2022) Polynomial Wiener LQG Controllers based on Toeplitz Matrices. Journal of Physics: Conference Series 2224:1, pages 012114.
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Nguyen Cong Danh. (2021) Adjusting LQG with Noise Signals, PID Controller for Acrobot System. Mathematical Problems in Engineering 2021, pages 1-13.
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Lalitesh Kumar, Prawendra Kumar & Sukhwinder Singh Dhillon. (2020) A multiobjective optimization approach for linear quadratic Gaussian/loop transfer recovery design. Optimal Control Applications and Methods 41:4, pages 1267-1287.
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Michael J. Grimble & Paweł MajeckiMichael J. Grimble & Paweł Majecki. 2020. Nonlinear Industrial Control Systems. Nonlinear Industrial Control Systems 247 290 .
Michael J. Grimble & Paweł MajeckiMichael J. Grimble & Paweł Majecki. 2020. Nonlinear Industrial Control Systems. Nonlinear Industrial Control Systems 65 125 .
Mohamed Redouane Kafi, Hicham Chaoui, Suruz Miah & Abderrazak Debilou. (2017) Local model networks based mixed-sensitivity H-infinity control of CE-150 helicopters. Control Theory and Technology 15:1, pages 34-44.
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Huijun Gao & Xianwei LiHuijun Gao & Xianwei Li. 2014. Robust Filtering for Uncertain Systems. Robust Filtering for Uncertain Systems 1 22 .
H. F. Wahab, R. Katebi & R. Villanova. (2012) Comparisons of nonlinear estimators for wastewater treatment plants. Comparisons of nonlinear estimators for wastewater treatment plants.
A. S. Matveev. (2006) Theory of optimal control in the works of V.A. Yakubovich. Automation and Remote Control 67:10, pages 1645-1698.
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Michael J. Grimble. 2006. Robust Industrial Control Systems. Robust Industrial Control Systems 113 165 .
Michael J. Grimble. 2006. Robust Industrial Control Systems. Robust Industrial Control Systems 57 111 .
Michael J. Grimble. 2006. Robust Industrial Control Systems. Robust Industrial Control Systems 1 55 .
I.M. Bachilina & S.A. Stepanov. (2000) Robust Stabilization of Uncertain Continuous-Time and Discrete-Time Systems. IFAC Proceedings Volumes 33:16, pages 35-39.
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A. S. Matveev & V. A. Yakubovich. (2000) Nonconvex global optimization problems in control theory. Journal of Mathematical Sciences 100:5, pages 2531-2563.
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M. J. Grimble. (1998) 3 1/2 DOF Polynomial Solution of the Inferential H2/H∞ Control Problem With Application to Metal Rolling. Journal of Dynamic Systems, Measurement, and Control 120:4, pages 445-455.
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K.-C. Han, K.-W. Han, J.-W. Perng & S.-J. Tsai. (1998) State–space solution of the standard H∞ control problem for strip mill gauge control. IEE Proceedings - Control Theory and Applications 145:3, pages 291-298.
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D.S. Desanj, M.J. Grimble & M.R. Katebi. (2016) State-space adaptive H∞ controller with application to a ship control system. Transactions of the Institute of Measurement and Control 19:3, pages 139-153.
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M. J. Grimble & M. R. Katebi. 1996. Polynomial Methods for Control Systems Design. Polynomial Methods for Control Systems Design 223 251 .
Jeffrey A. Abler & Paul I. Ro. (1994) Directional damping control: vibration reduction and optimality for precision slide motion. Precision Engineering 16:2, pages 84-98.
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Quan Ma & P.I. Ro. (1994) Robust H/sub ∞/ control of a traction drive system for precision motion. Robust H/sub ∞/ control of a traction drive system for precision motion.
Vladimír Kučera. (1993) Diophantine equations in control—A survey. Automatica 29:6, pages 1361-1375.
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Gilead Tadmor. (1993) The Standard $H_\infty $ Problem and the Maximum Principle: The General Linear Case. SIAM Journal on Control and Optimization 31:4, pages 813-846.
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M.J. Grimble. (1992) Model reference predictive LQG optimal control law for SIMO systems. IEEE Transactions on Automatic Control 37:3, pages 365-371.
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V. B. Larin. (1992) Optimization in the hardy space and the problem of the parametrization of controllers (survey). International Applied Mechanics 28:2, pages 67-84.
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A. A. Stoorvogel. (1992) The Discrete Time $H_\infty $ Control Problem with Measurement Feedback. SIAM Journal on Control and Optimization 30:1, pages 182-202.
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B. Connor, S.N. Iyer, W.E. Leithead & M.J. Grimble. (1992) Control of a horizontal axis wind turbine using H infinity control. Control of a horizontal axis wind turbine using H infinity control.
M. W. Foley & T. J. Harris. (2006) Structure and performance of discrete H ∞ optimal control . Optimal Control Applications and Methods 13:1, pages 1-27.
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D. Fragopoulos, M.J. Grimble & U. Shaked. (1991) H/sub infinity / controller design for the SISO case using a Wiener approach. IEEE Transactions on Automatic Control 36:10, pages 1204-1208.
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I. Yaesh & U. Shaked. (1991) Two-degree-of-freedom H/sub infinity /-optimization of multivariable feedback systems. IEEE Transactions on Automatic Control 36:11, pages 1272-1276.
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I. Yaesh & U. Shaked. (1991) A transfer function approach to the problems of discrete-time systems: H/sub infinity /-optimal linear control and filtering. IEEE Transactions on Automatic Control 36:11, pages 1264-1271.
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M.J. Grimble. (1991) H/sub infinity / fixed-lag smoothing filter for scalar systems. IEEE Transactions on Signal Processing 39:9, pages 1955-1963.
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M. J. Grimble. 1991. Advanced Methods in Adaptive Control for Industrial Applications. Advanced Methods in Adaptive Control for Industrial Applications 43 60 .
K J Hunt & P J Gawthrop. 1991. Advanced Methods in Adaptive Control for Industrial Applications. Advanced Methods in Adaptive Control for Industrial Applications 21 30 .
G. Conte, A. M. Perdon & B. WymanA. Casavola & E. Mosca. 1991. New Trends in Systems Theory. New Trends in Systems Theory 194 201 .
M.J. Grimble & A. El Sayed. (1990) Solution of the H/sub infinity / optimal linear filtering problem for discrete-time systems. IEEE Transactions on Acoustics, Speech, and Signal Processing 38:7, pages 1092-1104.
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O.A. Sebakhy. (1990) Comments on "Ripple-free deadbeat control of SISO discrete systems" by H.R. Sirisena. IEEE Transactions on Automatic Control 35:6, pages 765-766.
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M.J. Grimble. (1990) Comments on Stein's postulated high-frequency behavior of H/sub infinity / optimal controllers. IEEE Transactions on Automatic Control 35:6, pages 762-765.
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M.J. Grimble, D. Ho & A. Elsayed. (1990) H ∞ Robust Linear Estimator. IFAC Proceedings Volumes 23:1, pages 477-482.
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M.J. Grimble & N.A. Fairbairn. (1990) The F-Iteration Approach to H ∞ Control. IFAC Proceedings Volumes 23:1, pages 199-204.
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A. Sideris. (1990) H/sub infinity / optimal control as a weighted Wiener-Hopf problem. IEEE Transactions on Automatic Control 35:3, pages 361-366.
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M.J. Grimble. (1990) Relationship between the trace and maximum eigenvalue norms for linear quadratic control design. IEEE Transactions on Automatic Control 35:10, pages 1176-1181.
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E. Mosca, A. Casavola & L. Giarre'. (1990) Minimax LQ stochastic tracking and servo problems. IEEE Transactions on Automatic Control 35:1, pages 95-97.
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M.J. Grimble, D. Ho & A. Elsayed. 1990. Adaptive Systems in Control and Signal Processing 1989. Adaptive Systems in Control and Signal Processing 1989 477 482 .
M.J. Grimble & N.A. Fairbairn. 1990. Adaptive Systems in Control and Signal Processing 1989. Adaptive Systems in Control and Signal Processing 1989 199 204 .
D. Ho, U. Shaked, M. J. Grimble & A. Elsayed. 1990. Robust Control of Linear Systems and Nonlinear Control. Robust Control of Linear Systems and Nonlinear Control 387 395 .
M.J. Grimble. (1989) Minimization of a combined H∞ and LQG cost-function for a two-degrees-of-freedom control design. Automatica 25:4, pages 635-638.
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D.S. Bernstein & W.M. Haddad. (1989) LQG control with an H/sup infinity / performance bound: a Riccati equation approach. IEEE Transactions on Automatic Control 34:3, pages 293-305.
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U. Shaked & I. Yaesh. (1989) Frequency domain H/sub ∞ - optimization of multivariable feedback systems. Frequency domain H/sub ∞ - optimization of multivariable feedback systems.
E. Mosca & L. Giarre. (1989) Minimax LQ stochastic tracking and disturbance rejection problems. Minimax LQ stochastic tracking and disturbance rejection problems.
I. Yaesh & U. Shaked. (1989) Minimum H/sub infinity /-norm regulation of linear discrete-time systems and its relation to linear quadratic discrete games. Minimum H/sub infinity /-norm regulation of linear discrete-time systems and its relation to linear quadratic discrete games.
M. Saeki. (1989) Methods of solving a polynomial equation for an H/sub infinity / optimal control problem for a single-input single-output discrete-time system. IEEE Transactions on Automatic Control 34:2, pages 166-168.
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A. Elsayed, M.J. Grimble & D. Ho. (1988) On H/sub infinity / filtering in multivariable discrete-time systems. On H/sub infinity / filtering in multivariable discrete-time systems.
N.A. Fairbairn & M.J. Grimble. (1988) A scalar H/sub infinity / explicit adaptive controller. A scalar H/sub infinity / explicit adaptive controller.
M.J. Grimble. (1988) Model reference predictive LQC optimal control law for SIMO systems. Model reference predictive LQC optimal control law for SIMO systems.
G. Brown, M. Grimble & D. Biss. (1987) A simple, efficient H<sub>&#x0221E;</sub> controller algorithm. A simple, efficient H<sub>&#x0221E;</sub> controller algorithm.
Athanasios Sideris & Davut Kavranoglu. (1987) H<sub>&#x0221E;</sub> optimal control as weighted Weiner-Hopf optimization. H<sub>&#x0221E;</sub> optimal control as weighted Weiner-Hopf optimization.
T. J. Harris & J. F. Macgregor. (2004) Design of multivariable linear‐quadratic controllers using transfer functions. AIChE Journal 33:9, pages 1481-1495.
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M.A. Hersh. (1987) H ∞ Filtering of Multivariable Systems. IFAC Proceedings Volumes 20:5, pages 37-42.
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M. Saeki, M. J. Grimble, E. Kornegoor & M. A. Johnson. 1987. Modelling, Robustness and Sensitivity Reduction in Control Systems. Modelling, Robustness and Sensitivity Reduction in Control Systems 357 379 .
Edmond A. Jonckheere & Jyh-Ching Juang. 1987. Modelling, Robustness and Sensitivity Reduction in Control Systems. Modelling, Robustness and Sensitivity Reduction in Control Systems 323 356 .

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