Previous |  Up |  Next

Article

Title: Nonregular decoupling with stability of two-output systems (English)
Author: Ruiz-León, Javier
Author: Muñoz, Jorge A. Torres
Author: Lizaola, Francisco
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 38
Issue: 5
Year: 2002
Pages: [553]-569
Summary lang: English
.
Category: math
.
Summary: In this paper we present a solution to the decoupling problem with stability of linear multivariable systems with 2 outputs, using nonregular static state feedback. The problem is tackled using an algebraic-polynomial approach, and the main idea is to test the conditions for a decoupling compensator with stability to be feedback realizable. It is shown that the problem has a solution if and only if Morse’s list $I_{2}$ is greater than or equal to the infinite and unstable structure of the proper and stable part of the stable interactor of the system. A constructive procedure to find a state feedback, which achieves decoupling with stability, is also presented. (English)
Keyword: linear multivariable system
Keyword: decoupling
Keyword: stability
MSC: 93B11
MSC: 93B15
MSC: 93C35
MSC: 93D05
MSC: 93D15
idZBL: Zbl 1265.93203
idMR: MR1966945
.
Date available: 2009-09-24T19:48:42Z
Last updated: 2015-03-25
Stable URL: http://hdl.handle.net/10338.dmlcz/135486
.
Reference: [1] Descusse J., Dion J. M.: On the structure at infinity of linear square decoupled systems.IEEE Trans. Automat. Control AC-27 (1982), 971–974 Zbl 0485.93042, MR 0680500, 10.1109/TAC.1982.1103041
Reference: [2] Descusse J., Lafay J. F., Malabre M.: Solution of the static-state feedback decoupling problem for linear systems with two outputs.IEEE Trans. Automat. Control AC-30 (1985), 914–918 Zbl 0566.93010, MR 0799492, 10.1109/TAC.1985.1104089
Reference: [3] Descusse J., Lafay J. F., Malabre M.: Solution to Morgan’s problem.IEEE Trans. Automat. Control 33 (1988), 732–739 Zbl 0656.93018, MR 0950794, 10.1109/9.1289
Reference: [4] Dion J. M., Commault C.: The minimal delay decoupling problem: Feedback implementation with stability.SIAM J. Control Optim. 26 (1988), 66–82 Zbl 0646.93049, MR 0923304, 10.1137/0326005
Reference: [5] Falb P. L., Wolovich W. A.: Decoupling in the design and synthesis of multivariable control systems.IEEE Trans. Automat. Control AC-12 (1967), 651–659 10.1109/TAC.1967.1098737
Reference: [6] Herrera A.: Sur le decouplage des systemes lineaires par des lois statiques non regulieres.PhD Thesis, Université de Nantes, Ecole Centrale Nantes 1991
Reference: [7] Herrera A., Torres J. A., Ruiz-León J.: The nonregular Morgan’s problem: A polynomial solution for the case of two outputs.In: Proc. European Control Conference (ECC’93), Groningen 1993, pp. 2275–2278
Reference: [8] G. J. C. Martínez, Malabre M.: The row by row decoupling problem with stability: A structural approach.IEEE Trans. Automat. Control 39 (1994), 2457–2460 Zbl 0825.93252, MR 1337570, 10.1109/9.362849
Reference: [9] Morse A. S.: Structural invariants of linear multivariable systems.SIAM J. Control 11 (1973), 446–465 Zbl 0259.93011, MR 0386762, 10.1137/0311037
Reference: [10] Ruiz-León J., Zagalak, P., Eldem V.: On the Morgan problem with stability.Kybernetika 32 (1996), 425–441 MR 1420133
Reference: [11] Vidyasagar M.: Control System Synthesis: A Factorization Approach.MIT Press, Cambridge, MA 1985 Zbl 0655.93001, MR 0787045
Reference: [12] Wolovich W. A., Falb P. L.: Invariants and canonical forms under dynamic compensation.SIAM J. Control Optim. 14 (1976), 996–1008 Zbl 0344.93019, MR 0424306, 10.1137/0314063
.

Files

Files Size Format View
Kybernetika_38-2002-5_5.pdf 2.754Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo