Model reduction of complex systems in the linear-fractional framework

This paper discusses model reduction for systems in several different classes, in particular time-varying, multidimensional or uncertain systems, and nonlinear systems in the linear-fractional framework. We describe in detail the unifying viewpoint that this framework provides to all of these classes, and discuss the numerical methods used to construct reduced-order models. The methods used are extensions of the well-known method of balanced truncation, with provably good properties in the induced-norm.

[1]  Jerrold E. Marsden,et al.  Empirical model reduction of controlled nonlinear systems , 1999, IFAC Proceedings Volumes.

[2]  Geir E. Dullerud,et al.  Guaranteed error bounds for model reduction of linear time-varying systems , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[3]  Geir E. Dullerud,et al.  A new approach for analysis and synthesis of time-varying systems , 1999, IEEE Trans. Autom. Control..

[4]  Fernando Paganini,et al.  Analysis of implicitly defined systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[5]  J. M. A. Scherpen,et al.  Balancing for nonlinear systems , 1993 .

[6]  P. Gahinet,et al.  A Convex Characterization of Gain-Scheduled H-Infinity Controllers (Vol 40, Pg 853, 1995) , 1995 .

[7]  Carolyn L. Beck.  Model reduction and minimality for uncertain systems , 1997 .

[8]  P. Gahinet,et al.  A convex characterization of gain-scheduled H∞ controllers , 1995, IEEE Trans. Autom. Control..

[9]  John Doyle,et al.  A necessary and sufficient minimality condition for uncertain systems , 1999, IEEE Trans. Autom. Control..

[10]  A. Yousuff,et al.  Model reduction of mechanical systems , 1993 .

[11]  S. Bittanti,et al.  The Periodic Riccati Equation , 1991 .

[12]  Carolyn L. Beck,et al.  On the role of LFT model reduction methods in robust controller synthesis for a pressurized water reactor , 1999, IEEE Trans. Control. Syst. Technol..

[13]  A. Megretski.  Necessary and sufficient conditions of stability: a multiloop generalization of the circle criterion , 1993, IEEE Trans. Autom. Control..

[14]  A. Packard.  Gain scheduling via linear fractional transformations , 1994 .

[15]  J. Shamma.  Robust stability with time-varying structured uncertainty , 1994, IEEE Trans. Autom. Control..

[16]  Carolyn L. Beck,et al.  Model reduction of multidimensional and uncertain systems , 1994, IEEE Trans. Autom. Control..

[17]  A. Packard,et al.  Optimal, constant I/O similarity scaling for full-information and state-feedback control problems , 1992 .