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Structured coprime factor model reduction based on LMIs. (English) Zbl 1067.93010
The authors of the paper under review study model reduction methods that preserve a certain structure of the linear dynamical system. They present two approaches that are based on expansive and contracting factorizations. Finally, the authors give an example that illustrates the technique developed in the paper.

##### MSC:
 93B11 System structure simplification 15A39 Linear inequalities of matrices
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##### References:
 [1] Anderson, B.D.O.; Liu, Y., Controller reductionconcepts and approaches, IEEE transactions on automatic control, 34, 802-812, (1989) · Zbl 0698.93034 [2] Beck, C.L.; Doyle, J.C.; Glover, K., Model reduction of multi-dimensional and uncertain systems, IEEE transactions on automatic control, 41, 1466-1477, (1996) · Zbl 0862.93009 [3] Beck, C. L., & Bendottii, P., (1997). Model reduction methods for unstable uncertain systems. In Proceedings of 1997 CDC, pp. 3298-3303. [4] Dullerud, G.E.; Paganini, F., A course in robust control theory: a convex approach, (2000), Springer New York · Zbl 0939.93001 [5] El-Zobaidi, H., & Jaimoukha, I. (1998). Robust control and model and controller reduction of linear parameter varying system. In Proceedings of 1998 CDC, pp. 3015-3020. [6] Enns, D. F., (1984). Model reduction with balanced realizations: an error bound and frequency weighted generalization. In Proceedings of 1984 CDC, pp. 802-812. [7] Georgiou, T.; Smith, M., Optimal robustness in the gap metric, IEEE transactions on automatic control, 35, 673-686, (1990) · Zbl 0800.93289 [8] Glover, K., All optimal Hankel-norm approximations of linear multivariable systems and their $$L_\infty$$ error bounds, International journal of control, 39, 1115-1193, (1984) · Zbl 0543.93036 [9] Li, L., & Paganini, F. (2002). LMI approach to structured model reduction via coprime factorizations. In Proceedings of 2002 ACC, pp. 1174-1179. [10] Li, L., & Paganini, F. (2003). Structured frequency weighted model reduction. In Proceedings of 2003 CDC, pp. 2841-2846. [11] Liu, Y.; Anderson, B.D.O., Controller reduction via stable factorization and balancing, International journal of control, 44, 507-531, (1986) · Zbl 0604.93020 [12] McFarlane, D.C.; Glover, K., robust controller design using normalized coprime factor plant descriptions, (1990), Springer Berlin, New York · Zbl 0688.93044 [13] Meyer, D.G., Fractional balanced reductionmodel reduction via fractional representation, IEEE transactions on automatic control, 35, 1341-1345, (1990) · Zbl 0723.93011 [14] Moore, B.C., Principal component analysis in linear systemscontrollability, observablity, and model reduction, IEEE transactions on automatic control, 26, 17-32, (1981) [15] Tsai, Y.K.; Narasimhamurthi, N.; Wu, F.F., Structure-preserving model reduction with applications to power system dynamic equivalents, IEEE transactions on circuits and systems, CAS-29, 525-535, (1982) · Zbl 0495.93008 [16] Vinnicombe, G., Frequency domain uncertainty and the graph topology, IEEE transactions on automatic control, 38, 1371-1383, (1993) · Zbl 0787.93076 [17] Wood, G. D., Goddard, P. J., & Glover, K. (1996). Approximation of linear parameter-varying systems. In Proceedings of 1996 CDC, pp. 406-411. [18] Zhou, K.; D’Souza, C.; Cloutier, J.R., Structurally balanced controller order reduction with guaranteed closed loop performance, Systems and control letters, 24, 235-242, (1995) · Zbl 0877.93013 [19] Zhou, K.; Doyle, J.C.; Glover, K., robust and optimal control, (1996), Prentice-Hall Upper Saddle River, NJ · Zbl 0999.49500
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