Optimal Routh approximations for continuous-time systems

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Abstract
A new combination of Routh stability criterion and integral squared error (ISE) criterion approach is proposed for the linear model reduction of high-order dynamic systems. The method consists of a two-step computational scheme. In the first step, the Routh approximation method is used to reduce the order of the denominator polynomial of the system transfer function. In the second step, the Routh table is used to derive a set of optimal coefficients of the numerator polynomial of reduced model such that the ISE between the unit step responses of the original and simplified system is reduced to a minimum. The advantages of the proposed method are that it does not actually evaluate the system time response in the step of minimizing the ISE, and the reduced model is stable if the original system is stable.

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