×

A note on interconnections. (English) Zbl 1228.93033

Summary: The regular interconnection problem is considered in the context of Fliess models defined over an arbitrary Noetherian ring. It is shown that the problem always has a solution provided that the plant is strongly controllable.

MSC:

93B25 Algebraic methods
93B05 Controllability
Full Text: DOI

References:

[1] Kuijper, M., Why do stabilizing controllers stabilize?, Automatica, 31, 621-625 (1995) · Zbl 0824.93048
[2] Willems, J. C., On interconnections, control, and feedback, IEEE Trans. Automat. Control, 42, 326-339 (1997) · Zbl 0872.93034
[3] Rocha, P.; Wood, J., Trajectory control and interconnection of 1D and nD systems, SIAM J. Control Optim., 40, 107-134 (2001) · Zbl 1030.93033
[4] Fliess, M., Some basic structural properties of generalized linear systems, Systems Control Lett., 15, 391-396 (1990) · Zbl 0727.93024
[5] Bisiacco, M.; Valcher, M., A note on the direct sum decompositions of two-dimensional behaviors, IEEE Trans. Circuits Syst., 48, 490-494 (2001) · Zbl 1006.93012
[6] Rocha, P., Feedback control of multidimensional behaviors, Systems Control Lett., 45, 207-215 (2002) · Zbl 1073.93529
[7] Trentelman, H. L.; Napp Avelli, D., On the regular implementability of \(n\) D systems, Systems Control Lett., 56, 265-271 (2007) · Zbl 1113.93049
[8] Zerz, E.; Lomadze, V., A constructive solution to interconnection and decomposition problems with multidimensional behaviors, SIAM J. Control Optim., 40, 1072-1086 (2001) · Zbl 1030.93012
[9] J.F. Pommaret, A. Quadrat, Equivalences of linear control systems, Proc. MTNS 2000, Perpignan, 2000.; J.F. Pommaret, A. Quadrat, Equivalences of linear control systems, Proc. MTNS 2000, Perpignan, 2000. · Zbl 0971.93017
[10] Fliess, M.; Mounier, H., Controllability and observability of linear delay systems: an algebraic approach, ESAIM Control Optim. Calc. Var., 3, 301-314 (1998) · Zbl 0908.93013
[11] Fliess, M.; Bourlès, H., Discussing some examples of linear system interconnections, Systems Control Lett., 27, 1-7 (1996) · Zbl 0877.93064
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.