Based on a method for right coprime factorisations of linear systems using matrix elementary transformations, it is shown that a very simple iteration formula exists for right coprime factorisations of multi-input linear systems in system upper Hessenberg forms. This formula gives directly the coefficient matrices of the pair of solutions to the right coprime factorisation of the system Hessenberg form, and involves only inverses of a few triangular matrices and some matrix products and summations. Based on this formula, a simple, efficient procedure for determining a right coprime factorisation of a multi-input linear system is proposed, which first converts a given linear system into its system Hessenberg form using some orthogonal similarity transformations and then applies the iteration formula to the converted system Hessenberg form. An example demonstrates the use of the approach.
References
-
-
1)
-
DUAN, G.R., PATTON, R.J.: `Robust fault detection in linear systems using Luenberger observers', Proceedings of International Conference on CONTROL '98, 1–4 September 1998, Swansea, UK, 2, p. 1468–1473.
-
2)
-
G.R. DUAN ,
R.J. PATTON
.
Eigenstructure assignment in descriptor systems via state feedback---a new complete parametric approach.
Int. J. Syst. Sci.
,
2 ,
167 -
178
-
3)
-
G.R. DUAN
.
Eigenstructure assignment by decentralized output feedback––a complete parametric approach.
IEEE Trans. Autom. Control
,
5 ,
1009 -
1014
-
4)
-
DUAN, G.R., PATTON, R.J., CHEN, J., CHEN, Z.: `A parametric approach for robust fault detection in linear systems with unknown disturbances', Proceedings of IFAC Symposium on Fault detection, supervision and safety for technical processes, SAFEPROCESS'97, 26–28 August 1997, Kingston Upon Hull, UK, p. 318–322.
-
5)
-
G.R. Duan
.
Parametric approach for eigenstructure assignment in descriptor systems via output feedback.
IEE Proc., Control Theory Appl.
,
6 ,
36 -
41
-
6)
-
G.R. Duan
.
Robust eigenstructure assignment via dynamical compensators.
Automatica
,
2 ,
469 -
474
-
7)
-
DUAN, G.R., MA, K.M.: `Robust Luenberger function observers for linear systems', Preprints of IFAC Youth Automatic Conference (IFAC YAC'95, 22–25 August 1995, Beijing, China, p. 382–387.
-
8)
-
G.R. Duan
.
Solution to matrix equation AV+BW=EVF and eigenstructure assignment for descriptor systems.
Automatica
,
3 ,
639 -
643
-
9)
-
N.F. ALMUTHAIRI ,
S. BINGULAC
.
On coprime factorization and minimal-realization of transfer-function matrices using the pseudo-observability concept.
Int. J. Syst. Sci.
,
27 ,
1819 -
1844
-
10)
-
G.R. Duan
.
On the solution to Sylvester matrix equation AV+BW=EVF.
IEEE Trans. Autom. Control
,
4 ,
612 -
614
-
11)
-
M. GREEN
.
H-infinity controller synthesis by J-lossless coprime factorization.
SIAM J. Control Optim.
,
3 ,
522 -
547
-
12)
-
G.R. DUAN
.
A simple algorithm for robust eigenvalue assignment in linear output feedback.
IEE Proc.-D
,
5 ,
465 -
469
-
13)
-
K. OHISHI ,
T. MIYAZAKI ,
Y. NAKAMURA
.
High performance ultra-low speed servo system based on doubly coprime factorization and instantaneous speed observer.
IEEE-ASME Trans. Mechatronics
,
1 ,
89 -
98
-
14)
-
G.R. DUAN ,
R.J. PATTON
.
Eigenstructure assignment in descriptor systems via proportional plus derivative state feedback.
Int. J. Control
,
5 ,
1147 -
1162
-
15)
-
DUAN, G.R., ZHOU, L.S., XU, Y.M.: `A parametric approach for observer-based control system design', Proceeding of Asia-Pacific Conference on Measurement and control, 21–23 August 1991, Guangzhou, China, p. 295–300.
-
16)
-
A.J. LAUB ,
A. LINNEMANN
.
Hessenberg and Hessenberg triangular forms in linear system theory.
Int. J. Control
,
6 ,
1523 -
1547
-
17)
-
P.M.M. BONGERS ,
P.S.C. HEUBERGER
.
(1990)
Discrete normalized coprime factorization, .
-
18)
-
T.G.J. BEELEN ,
G.W. VELTKAMP
.
Numerical computation of a coprime factorization of a transfer-function matrix.
Syst. Control Lett.
,
4 ,
281 -
288
-
19)
-
G.R. Duan
.
Eigenstructure assignment and response analysis in descriptor linear systems with state feedback control.
Int. J. Control
,
5 ,
663 -
694
-
20)
-
S. BINGULAC ,
N.F. ALMUTHAIRI
.
Novel-approach to coprime factorization and minimal-realization of transfer-function matrices.
J. University of Kuwait-Science
,
1 ,
24 -
43
-
21)
-
G.R. DUAN
.
Solution to matrix equation AV+BW=VF and their application to eigenstructure assignment in linear systems.
IEEE Trans. Autom. Control
,
2 ,
276 -
280
-
22)
-
E.S. ARMSTRONG
.
Coprime factorization approach to robust stabilization of control-structures interaction evolutionary model.
J. Guid. Control Dyn.
,
5 ,
935 -
941
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