A program for solving the L2 reduced-order model problem with fixed denominator degree

A set of necessary conditions that must be satisfied by the L2 optimal rational transfer matrix approximating a given higher-order transfer matrix, is briefly described. On its basis, an efficient iterative numerical algorithm has been obtained and implemented using standard MATLAB functions. The purpose of this contribution is to make the related computer program available and to illustrate some significant applications.

[1]  S. Mukherjee,et al.  Reduced order modelling of linear multivariable systems using an error minimization technique , 1988 .

[2]  K. Åström Introduction to Stochastic Control Theory , 1970 .

[3]  F. R. Gantmakher The Theory of Matrices , 1984 .

[4]  D. Bernstein,et al.  Homotopy Methods for Solving the Optimal Projection Equations for the H2 Reduced Order Model Problem , 1992 .

[5]  R. Langer Interpolation and Approximation by Rational Functions in the Complex Domain , 1937 .

[6]  P. Aigrain,et al.  Synthesis of n‐Reactance Networks for Desired Transient Response , 1949 .

[7]  Gian Antonio Mian,et al.  On model reduction by L2-optimal pole retention , 1990 .

[8]  D. Wilson,et al.  A new algorithm for optimal reduction of multivariable systems , 1980 .

[9]  Gian Antonio Mian,et al.  Optimality conditions in multivariable L2 model reduction , 1993 .

[10]  M. Olivi,et al.  Approximation rationnelle en norme L2 des systèmes dynamiques , 1990 .

[11]  Jer-Nan Juang,et al.  Model reduction for flexible structures , 1990 .

[12]  Y. Shamash Linear system reduction using Pade approximation to allow retention of dominant modes , 1975 .

[13]  Martine Olivi,et al.  Identification and rational L2 approximation A gradient algorithm , 1991, Autom..

[14]  L. Meier,et al.  Approximation of linear constant systems , 1967, IEEE Transactions on Automatic Control.

[15]  John T. Spanos,et al.  A new algorithm for L2 optimal model reduction , 1992, Autom..

[16]  C. P. Kwong,et al.  Optimal chained aggregation for reduced-order modeling† , 1982 .

[17]  D. Wilson Optimum solution of model-reduction problem , 1970 .

[18]  L. Baratchart Recent and new results in rational L 2-approximation , 1987 .

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

[20]  D. Bernstein,et al.  The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore , 1985 .

[21]  D. Wilson,et al.  Model reduction for multivariable systems , 1974 .

[22]  Arthur E. Bryson,et al.  Second-order algorithm for optimal model order reduction , 1990 .