Minimum Order Transfer Function: the Interpolation Approach

This paper presents an algorithm for obtaining the minimum order MISO transfer function model for the use in a model-based predictive controller. The source model can be either a non-minimal ARX model, a state-space model or any interconnection of linear models of mixed state-space and transfer function representations. The algorithm is based on polynomial interpolation theory, representing polynomials by their values on a set of points in the complex plane. Using this theory, we can find the minimum order from the dimension of the null space of a particular matrix. Finding the minimum order model is equivalent to finding a specific base of the null space. A novel feature of the presented approach is using a set of complex interpolation nodes obtained by mapping the standard set of real Chebyshev nodes by a bilinear transform.