×

Geometric minimization under external equivalence for implicit descriptions. (English) Zbl 0831.93010

A geometric characterization for the extremal minimality of an \((E, A, B, C)\) description for time-invariant linear systems is investigated. A minimization procedure from which a minimal realization can be obtained relies on very elementary operations using unitary transformations.

MSC:

93B20 Minimal systems representations
93B27 Geometric methods
93B11 System structure simplification
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aplevich, J. D., Minimal representations of implicit linear systems, Automatica, 21, 259-269 (1985) · Zbl 0565.93012
[2] Aplevich, J. D., Implicit Linear Systems, (Lecture Notes in Control and Information Sciences, Vol. 152 (1991), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0764.93001
[3] Bonilla, M.; Malabre, M., Non observable and redundant spaces for implicit descriptions, (Proc. 30th IEEE Conf. on Decision and Control, Brighton, U.K., 11-13 December 1991, Vol. 2 (1991)), 1425-1430
[4] Bonilla, M.; Malabre, M., Geometric characterizations of external minimality for implicit descriptions, (Proc. 32nd IEEE Conf. on Decision and Control, San Antonio, TX, Vol. 4 (1993)), 3311-3312
[5] Fliess, M., Geometric interpretation of the zeros and of the hidden modes of a constant linear system via a renewed realization theory, (Proc. IFAC Workshop on System Structure and Control: State Space and Polynomial Methods. Proc. IFAC Workshop on System Structure and Control: State Space and Polynomial Methods, Prague, September 1989 (1989)), 209-213
[6] Gantmacher, F. R., (Théorie des Matrices (1966), Dunod: Dunod Paris) · Zbl 0136.00410
[7] Kuijper, M., Descriptor representations without direct feedthrough term, Automatica, 28, 633-637 (1992) · Zbl 0766.93026
[8] Kuijper, M., First-order representations of linear systems, (PhD thesis (1992), Katholieke Univresiteit Brabant: Katholieke Univresiteit Brabant Amsterdam) · Zbl 0766.93026
[9] Kuijper, M.; Schumacher, J. M., Minimality of descriptor representations under external equivalence, Automatica, 27, 985-995 (1991) · Zbl 0777.93042
[10] Lewis, F. L., A tutorial on the geometric analysis of linear time-invariant implicit systems, Automatica, 28, 119-137 (1992) · Zbl 0745.93033
[11] Lewis, F. L.; Beauchamp, G., Computation of subspaces for singular systems, (Proc. MTNS’87. Proc. MTNS’87, Phoenix, 12, June (1987)) · Zbl 0725.93023
[12] Loiseau, J. J., Some geometric considerations about the Kronecker normal form, Int. J. Control, 42, 1411-1431 (1985) · Zbl 0609.93014
[13] Schumacher, J. M., Transformations of linear systems under external equivalence, Lin. Algebra Applics, 102, 1-34 (1988) · Zbl 0668.93019
[14] Willems, J. C., Input-output and state space representations of finite-dimensional linear time-invariant systems, Lin. Algebra Applics, 50, 581-608 (1983) · Zbl 0507.93017
[15] Wonham, W. M., (Linear Multivariable Control: A Geometric Approach (1985), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0609.93001
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.