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http://dx.doi.org/10.5302/J.ICROS.2002.8.5.351

A Balanced Model Reduction for Linear Parameter Varying Systems  

Yoo, Seog-Hwan (Dept.of Information Communication Engineering, Daegu University)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.8, no.5, 2002 , pp. 351-356 More about this Journal
Abstract
This papaer deals with a model reduction problem for linear systems with time varying parameters. For this problem, a controllability Grammian and an observability Grammian are introduced and computed by solving linear matrix inequalities. Using the controllability/observability Grammian, a balanced state space realization for linear parameter varying systems is obtained. From the balanced state space realization, a reduced model can be obtained by truncating not only states but also time varying parameters and an upper bound of the model reduction error is derived as well.
Keywords
linear parameter varying systems; controllability Grammian; observability Gramian; model reduction error; linear matrix inequality;
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  • Reference
1 L. Pernebo and L. M. Silverman, 'Modern reduction via balanced state space representations,' IEEE Trans. Automatic Control, vol. AC-27, no. 2, pp. 382-387, 1982   DOI
2 K. Glover, 'All optimal Hankel-norm approximations of linear multivariable systems and their L∞-error bounds,' Int. J. Control, vol. 39, no. 6, pp. 1115-1193, 1984   DOI   ScienceOn
3 G. A. Latham and B. D. O. Anderson, 'Frequency weighted optimal Hankel norm approximation of stable transfer functions,' Syst. Contr. Lett., vol. 5, no. 4, pp. 229-236, 1985   DOI   ScienceOn
4 B. D. O. Anderson, 'Weighted Hankel norm approximation: Calculation of bounds,' Syst. Contr. Lett., vol. 7, no. 4, pp. 247-255, 1986   DOI   ScienceOn
5 G. D. Wood, P. J. Goddard, and K. Glover, 'Approximation of linear parameter varying systems,' Proceedings of the 35th CDC, pp. 406-411, Kobe, Japan, Dec. 1996   DOI
6 C. L. Beck, J. Doyle, and K. Glover, 'Model reduction of multidimensional and uncertain systems,' IEEE Trans. Automatic Control, vol. 41, no. 10, pp. 1466-1477, 1996   DOI   ScienceOn
7 L. Xie, M. Fu, and de Souza, C. E., '$H_{\infty}$control and quadratic stabilization of systems with parameter uncertainty via output feedback,' IEEE Trans. Automatic Control, vol. AC-37, pp. 1253-1256, 1992   DOI   ScienceOn
8 P. Apkarian and P. Gahinet, 'A convex characterization of gain-scheduled $H_{infty}$controllers,' IEEE Trans. Automatic Control, vol. AC-40, no. 5, pp. 853-864, 1995   DOI   ScienceOn
9 Y. Liu and B. D. O. Anderson, 'Singular perturbation approximation of balanced systems,' Int. J. Control, vol. 50, pp. 1379-1405, 1989   DOI   ScienceOn
10 D. G. Meyer, 'Fractional balanced reduction: Model reduction via fractional epresentations,' IEEE Trans. Automatic Control, vol. AC-35, pp. 1341-1345, 1990   DOI   ScienceOn
11 I. Emre Kose and Jabbari, 'Disturbance attenuation for systems with real parametric uncertainty,' Proceedings of American Control Conference, Albuquerque, NM, June 1997   DOI