Optimal discrete model reduction by multipoint Padé approximation

Abstract A discrete-time multipoint Pade approximation method is presented that derives optimal reduced-order models. The method is seen to be easily implemented using a recently developed way of calculating Pade approximants. An important result that relates the optimal model to multipoint Pade approximation is proved and the whole process isseen to consist of multiplying matrices and solving linear equations. Numerical examples are given to illustrate the application of the new method.

[1]  Cornelius T. Leondes,et al.  Reduction of high-order discrete-time systems , 1988 .

[2]  Chyi Hwang,et al.  Simplification of z-transfer function via Padé approximation of tangent phase function , 1985 .

[3]  Y. Shamash,et al.  Reduction of discrete time systems using a modified Routh array , 1978 .

[4]  Adhemar Bultheel,et al.  Pade´ techniques for model reduction in linear system theory: a survey , 1986 .

[5]  S. Al-Assadi.  An iterative method for simplification of discrete systems , 1989 .

[6]  M. Milanese,et al.  A note on the derivation and use of reduced-order models , 1976 .

[7]  Y. Shamash.  Continued fraction methods for the reduction of discrete-time dynamic systems , 1974 .

[8]  T. T. Hartley,et al.  Least squares model reduction , 1992 .

[9]  T. N. Lucas.  Optimal model reduction by multipoint Padé approximation , 1993 .

[10]  Chyi Hwang,et al.  Order reduction of z-transfer functions via multipoint Jordan continued-fraction expansion , 1992 .

[11]  U. Al-Saggaf.  Approximation of discrete linear systems based on a dual criterion , 1991 .

[12]  Uri Shaked,et al.  Discrete multivariable system approximations by minimal Pade-type stable models , 1984 .

[13]  K. Han,et al.  Reduction of Transfer Functions by the Stability-Equation Method , 1979 .

[14]  T. N. Lucas.  Finding roots by deflated polynomial approximation , 1990 .

[15]  Magdi S. Mahmoud,et al.  Large scale systems modelling , 1981 .

[16]  H. Kimura.  Optimal L2-approximation with fixed poles , 1983 .

[17]  T. N. Lucas.  New matrix method for multipoint Padé approximation of transfer functions , 1993 .