Model comparison and simplification

In this paper we study the comparison and simplification of models given as linear fractional transformations on structured operator sets. Previous simplification results have generalised the method of balanced truncation to such models, including the computation of error bounds, based on solutions to linear matrix inequalities (LMIs). In this paper we show that the previously obtained error bounds hold for a much larger class of simplification methods. These new results can be interpreted as providing a generalisation of both balanced truncation and singular perturbation approximation in a single reduction algorithm.

[1]  R. D'Andrea,et al.  Kalman decomposition of linear fractional transformation representations and minimality , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

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

[3]  A. Rantzer,et al.  System Analysis via Integral Quadratic Constraints. Part II , 1997 .

[4]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

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

[6]  Megretski.  System Analysis via Integral Quadratic Constraints , Part , 1995 .

[7]  A. Rantzer,et al.  System analysis via integral quadratic constraints , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[8]  A. Megretski,et al.  Power Distribution Approach in Robust Control , 1993 .

[9]  K. Glover,et al.  Model reduction of LFT systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[10]  D. Hinrichsen,et al.  An improved error estimate for reduced-order models of discrete-time systems , 1990 .

[11]  B. Anderson,et al.  Singular perturbation approximation of balanced systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[12]  Robert E. Skelton,et al.  Model error concepts in control design , 1989 .

[13]  Gene F. Franklin,et al.  An error bound for a discrete reduced order model of a linear multivariable system , 1987 .

[14]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[15]  B. Anderson,et al.  Model reduction for control system design , 1984 .

[16]  K. Fernando,et al.  Singular perturbational model reduction in the frequency domain , 1982 .

[17]  K. Fernando,et al.  Singular perturbational model reduction of balanced systems , 1982 .

[18]  L. Silverman,et al.  Model reduction via balanced state space representations , 1982 .

[19]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .