Article
Full entry |
PDF
(1.8 MB)
Feedback
PDF
(1.8 MB)
Feedback
Keywords:
transfer matrix system; dynamic output feedback
transfer matrix system; dynamic output feedback
Summary:
Partial disturbance decoupling problems are equivalent to zeroing the first, say $k$ Markov parameters of the closed-loop system between the disturbance and controlled output. One might consider this problem when it is not possible to zero all the Markov parameters which is known as exact disturbance decoupling. Structured transfer matrix systems are linear systems given by transfer matrices of which the infinite zero order of each nonzero entry is known, while the associated infinite gains are unknown and assumed mutually independent. The aim in this paper is to derive the necessary and sufficient conditions for the generic solvability of the partial disturbance decoupling problem for structured transfer matrix systems, by dynamic output feedback. Generic solvability here means solvability for almost all possible values for the infinite gains of the nonzero transfer matrix entries. The conditions will be stated by generic essential orders which are defined in terms of minimal weight of the matchings in a bipartite graph associated with the structured transfer matrix systems.
References:
[1] Commault C., Dion J. M., Perez A.: Disturbance rejection for structured systems. IEEE Trans. Automat. Control AC–36 (1991), 884–887 DOI 10.1109/9.85072 | MR 1109830 | Zbl 0754.93023
[2] Commault C., Dion J. M., Benahcene M.: Output feedback disturbance decoupling graph interpretation for structured systems. Automatica 6 (1993), 1463–1472 DOI 10.1016/0005-1098(93)90010-Q | MR 1252963 | Zbl 0791.93040
[3] Commault C., Dion J. M., Benahcene M.: Decoupling and minimality of structured systems in a transfer matrix framework. In: Proc. IFAC Conference System Structure and Control, Nantes 1995, pp. 84–89
[4] Commault C., Dion J. M., Hovelaque V.: A geometric approach for structured systems: Application to disturbance decoupling. Automatica 3 (1997), 403–409 DOI 10.1016/S0005-1098(96)00186-0 | MR 1442558 | Zbl 0878.93015
[5] Eldem V., Özbay H., Selbuz H., Özçaldiran K.: Partial disturbance rejection with internal stability and $H_{\infty }$ norm bound. SIAM J. Control Optim. 36 (1998), 1, 180–192 DOI 10.1137/S0363012995287659 | MR 1616553 | Zbl 0915.93057
[6] Emre, E., Silverman L. H.: Partial model matching of linear systems. IEEE Trans. Automat. Control AC–25 (1980), 280–281 DOI 10.1109/TAC.1980.1102321 | MR 0567391 | Zbl 0432.93026
[7] Malabre M., Garcia J. C. M.: The partial model matching or partial disturbance rejection problem: geometric and structural solutions. IEEE Trans. Automat. Control 40 (1995), 2, 356–360 DOI 10.1109/9.341810 | MR 1312912 | Zbl 0823.93013
[8] Reinschke K. J.: Multivariable Control: A Graph Theoretic Approach. (Lecture Notes in Control and Information Sciences 108.) Springer–Verlag, Berlin 1988 MR 0962644 | Zbl 0682.93006
[9] Woude J. W. van der: On the structure at infinity of a structured system. Linear Algebra Appl. 148 (1991), 145–169 MR 1090758
[10] Woude J. W. van der: Disturbance decoupling by measurement feedback for structured systems: a graph theoretic approach. In: Proc. 2nd European Control Conf. ECC’93, Groningen 1993, pp. 1132–1137
[11] Woude J. W. van der: Disturbance decoupling by measurement feedback for structured transfer matrix systems. Automatica 32 (1996), 357–363 DOI 10.1016/0005-1098(95)00157-3 | MR 1379418
[12] Willems J. C., Commault C.: Disturbance decoupling by measurement feedback with internal stability or pole placement. SIAM J. Control Optim. 19 (1981), 490–504 DOI 10.1137/0319029 | MR 0618240
[13] Wonham W. M.: Linear Multivariable Control: A Geometric Approach. Third edition. Springer–Verlag, New York 1985 MR 0770574 | Zbl 0609.93001
Search
Partner of
