A new algorithm is presented for finding reduced-order models of the linear time-invariant systems. Proposed recursive algorithm minimizes a weighted mean squared impulse (or step) response error between the original system and the reduced order model. This proposed optimization algorithm require solving very easy linear equations rather than the usual complicated non-linear equations. The procedure guarantees a reduced order stable model at each recursive stage. Method is easily extended to multi-input/multi-output systems. Algorithm’s performance is compared with other methods reported in the literature.

Issue Section:
Technical Briefs
Topics:
Algorithms, Discrete time systems, Errors, Impulse (Physics), Nonlinear equations, Optimization algorithms, Time-invariant systems
1.
Anderson
B. O.
,
Jury
E. I.
, and
Mansour
M.
,
1986
, “
On Model Reduction of Discrete Time Systems
,”
Automatica
, Vol.
22
, pp.
717
–
721
.
2.
Grace, A., Laub, A., Little, J. N., and Thompson, C., 1990, “Control System Toolbox,” Matlab routine dbalreal.
3.
Bosley
M. J.
, and
Lees
F. P.
,
1972
, “
A Survey of Simple Transfer-Function Derivations from High-Order State Variable Models
,”
Automatica
, Vol.
8
, pp.
765
–
775
.
4.
Chen
M. H.
, and
Chang
J. Y.
,
1991
, “
Model Reduction for Continuous- and Discrete-Time Systems via Squared-Magnitude Response Matching by Linear Programming
,”
Int. Systems Set
, Vol.
22
, pp.
723
–
734
.
5.
Farsi
M.
,
Warwick
K.
, and
Guilandoust
M.
,
1986
, “
Stable Reduced-Order Models for Discrete-Time Systems
,”
IEE Proc. Pt. D Control Theory & Appl.
, Vol.
133
, pp.
137
–
141
.
6.
Fortunal, L., Nunari, G., and Gallo, A., 1992, Model Order Reduction Techniques with Applications in Electrical Engineering, Springer-Verlag, London.
7.
Genesio
R.
, and
Milanese
M.
,
1976
, “
A Note on the Derivation and Use of Reduced Order Models
,”
IEEE Trans. Auto. Contr.
, Vol.
21
, pp.
118
–
122
.
8.
Hill, D., 1988, Experiments in Computational Matrix Algebra, Random House, New York.
9.
Hsieh
C. S.
, and
Hwang
C.
,
1990
, “
Model Reduction for Linear Discrete-Time Systems Using Bilinear Schwarz Approximation
,”
Int. J. Systems Sci.
, Vol.
21
, pp.
33
–
49
.
10.
Jury, E. I., 1964, Theory and Application of the z-Transform Method, Wiley, New York.
11.
Laub, A., 1980, “Computation of Balancing Transformations,” Proc. JACC, Vol. 1, Paper FA8-E.
12.
Lim, M. T., 1994, “Order-Reduction Techniques for Modeling, Control and Filtering of Linear High Order Systems,” Ph.D thesis, Rutgers University, New Brunswick, NJ.
13.
Moore
B. C.
,
1981
, “
Principal Components Analysis in Linear Systems: Controllability, Observability, and Model Reduction
,”
IEEE Trans. Auto Contr.
, Vol.
AC–26
, no.
1
, pp.
17
–
32
.
14.
Porat
B.
, and
Freedlander
B.
,
1984
, “
An Efficient Algorithm for Output-Error Model Reduction
,”
Int. J. Control
, Vol.
39
, pp.
95
–
113
.
15.
Sanathanan
C. K.
, and
Koerner
J.
,
1963
, “
Transfer Function Synthesis as a Ratio of Two Complex Polynomials
,”
IEEE Trans. on Auto. Contr.
, Vol.
8
, pp.
56
–
58
.
16.
Steilitz
K.
, and
McBridge
L. E.
,
1965
, “
A Technique for the Identification of Linear Systems
.”
IEEE Trans. on Auto. Contr.
, Vol.
10
, pp.
461
–
464
.
17.
Shamash
Y.
,
1975
, “
Linear System Reduction Using Pade Approximation to Allow Retention of Dominant Modes
,”
Int. J. Control
, Vol.
21
, pp.
257
–
272
.
18.
Spanos
J. T.
,
Milman
M. H.
, and
Mingori
D. L.
,
1992
, “
A New Algorithm for L2 Optimal Model Reduction
,”
Automatica
, Vol.
28
, pp. 8
97
–
909
.
19.
Therapos
C. P.
,
1984
, “
Low-Order Modeling via Discrete Stability Equations
,”
IEE Pt. D Control Theory & Appl.
, Vol.
131
, pp.
248
–
252
.
20.
Warwick
K.
,
1984
, “
A New Approach to Reduced-Order Modeling
,”
IEE Pt. D Control Theory & Appl.
, Vol.
131
, pp.
74
–
78
.
21.
Wilson, D. A., “Optimum Solution of Model Reduction Problem,” IEE Pt. D Control Theory & Appl., Vol. 117–1165.
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