An improvement in stable Pade approximation using constrained minimization

In this paper, an improvement in Pade approximation is proposed to reduce the order of a linear-time-invariant higher order stable system, using the Hermite-Biehler stability theorem. Two free parameters are introduced in the denominator polynomial of the reduced model. It will be shown that for any positive values of these two parameters, the resulting reduced model will be stable. The numerator polynomial and these two parameters are obtained by matching time moments. In this proposed algorithm, the reduced model matches (r + 2) time moments exactly while (r + 3)-th moment is matched approximately. The proposed method is illustrated by two numerical examples.