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Title: Fixed poles of $H_2$ optimal control by measurement feedback (English)
Author: Camart, Jean-François
Author: del-Muro-Cuéllar, Basilio
Author: Malabre, Michel
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 38
Issue: 5
Year: 2002
Pages: [631]-642
Summary lang: English
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Category: math
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Summary: This paper is concerned with the flexibility in the closed loop pole location when solving the $H_2$ optimal control problem (also called the $H_2$ optimal disturbance attenuation problem) by proper measurement feedback. It is shown that there exists a precise and unique set of poles which is present in the closed loop system obtained by any measurement feedback solution of the $H_2$ optimal control problem. These “$H_2$ optimal fixed poles” are characterized in geometric as well as structural terms. A procedure to design $H_2$ optimal controllers which simultaneously freely assign all the remaining poles, is also provided. (English)
Keyword: measurement feedback solution
Keyword: fixed pole
MSC: 49N10
MSC: 93B27
MSC: 93B36
MSC: 93B52
MSC: 93B55
MSC: 93B60
idZBL: Zbl 1265.93115
idMR: MR1966951
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Date available: 2009-09-24T19:49:28Z
Last updated: 2015-03-25
Stable URL: http://hdl.handle.net/10338.dmlcz/135492
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Reference: [1] Basile G., Marro G.: Controlled and Conditioned Invariants in Linear System Theory.Prentice Hall, Englewood Cliffs, N.J. 1992 Zbl 0758.93002, MR 1149379
Reference: [2] Boyd S., Ghaoui L. El, Feron, E., Balakrishnan V.: Linear Matrix Inequalities in System and Control Theory.SIAM Stud. Appl. Math. 15 (1994) Zbl 0816.93004, MR 1284712
Reference: [3] Del-Muro-Cuellar B., Malabre M.: Fixed poles of disturbance rejection by dynamic measurement feddback: a geometric approach.Automatica 37 (2001), 2, 231–238 MR 1832029, 10.1016/S0005-1098(00)00157-6
Reference: [4] Chen B. M., Saberi A., Sannuti, P., Shamash Y.: Construction and parametrization of all static and dynamic ${H}_2$ optimal state feedback solutions, optimal fixed modes, and fixed decoupling zeros.IEEE Trans. Automat. Control 38 (1993), 2, 248–261 MR 1206805, 10.1109/9.250513
Reference: [5] Malabre M., Kučera V.: Infinite structure and exact model matching problem: a geometric approach.IEEE Trans. Automat. Control AC-29 (1984), 3, 266–268 10.1109/TAC.1984.1103502
Reference: [6] Morse A. S.: Output controllability and system synthesis.SIAM J. Control 9 (1971), 2, 143–148 Zbl 0222.93006, MR 0290819, 10.1137/0309012
Reference: [7] Saberi A., Sannuti, P., Chen B. M.: ${H}_2$ Optimal Control.Prentice Hall, Englewood Cliffs, N.J. 1995
Reference: [8] Saberi A., Sannuti, P., Stoorvogel A. A.: ${H}_2$ optimal controllers with measurement feedback for continuous-time systems-flexibility in closed-loop pole placement.Automatica 32 (1996), 8, 1201–1209 Zbl 1035.93503, MR 1409674
Reference: [9] Schumacher J. M.: Compensator synthesis using $(C,A,B)$-pairs.IEEE Trans. Automat. Control AC-25 (1980), 6, 1133–1138 Zbl 0483.93035, MR 0601495, 10.1109/TAC.1980.1102515
Reference: [10] Stoorvogel A. A.: The singular ${H}_2$ control problem.Automatica 28 (1992), 3, 627–631 MR 1166033, 10.1016/0005-1098(92)90189-M
Reference: [11] Stoorvogel A. A., Saberi, A., Chen B. M.: Full and reduced-order observer-based controller design for ${H}_2$-optimization.Internat. J. Control 58 (1993), 4, 803–834 MR 1239695, 10.1080/00207179308923030
Reference: [12] Willems J. C.: Almost invariant subspaces: An approach to high gain feedback design.Part I: Almost controlled invariant subspaces. IEEE Trans. Automat. Control AC-26 (1981), 1, 235–252 Zbl 0463.93020, MR 0609263, 10.1109/TAC.1981.1102551
Reference: [13] Willems J. C., Commault C.: Disturbance decoupling by measurement feedback with stability or pole placement.SIAM J. Control Optim. 19 (1981), 4, 409–504 Zbl 0467.93036, MR 0618240, 10.1137/0319029
Reference: [14] Wonham W. M.: Linear Multivariable Control: A Geometric Approach.Third edition. Springer Verlag, New York 1985 Zbl 0609.93001, MR 0770574
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