# Constrained suboptimal Pade model reduction

## Abstract

An extension of a recent Pad6 suboptimal model reduction method is presented which ensures that the initial time response values of the reduced models coincide with those for the full system for impulse or step inputs. This desirable property is seen to involve little extra computation and can be implemented on existing computer algebra packages. An example is given to illustrate its use. NOTATION denominator coefficients of G ( s) (n + k + 1) by (k + 1) coefficient matrix numerator coefficients of G(s) (n + k) by (k + 1) coefficient matrix k-dimensional vector elements of the vector c k-dimensional vector numerator coefficients of G&) (k + 1)-dimensional vector denominator coefficients of Gk(s) (k + 1) by (k + 1) matrix elements of the matrix F k by (k + 1) matrix system transfer function reduced kth-order transfer function first Markov parameter of G(s) m by m unit matrix integral square error index augmented integral square error index order of reduced model (n + k- i) by (n + k + 1- i) transformation matrix order of original system residues of G,(s) polynomial of degree (n + k- 1) Laplace transform variable transfer function of system transient step response transfer function of reduced model’s transient step response polynomial of degree (n + k) time response of original system time response of reduced model residues of G(s) Lagrange multiplier poles of G(s) poles Of G k ( S)