Order reduction of linear time invariant continuous systems using mixed approach

The proposed method of order reduction of linear time invariant continuous systems deals with determination of reduced system by equating the unit step responses of both the systems. First the denominator polynomial of the reduced system transfer function is found using the Differentiation method of order reduction. For finding the numerator polynomial, the unit step responses of both the systems are equated and power series expansion of exponentials occurring in both sides of the equation is done and then by equating the coefficients of all the powers of t, the residues are determined to finally find the numerator polynomial coefficients and reduced system transfer function. Only linear systems of equations are required to be solved in the proposed method¹.