Reduced-order models of 2-D linear discrete separable-denominator system using bilinear Routh approximations

The authors extend the Routh approximation method for one-dimensional (1-D) discrete systems to two-dimensional (2-D) discrete systems for finding stable reduced-order models from a stable high-order 2-D linear discrete separable-denominator system (SDS). The extension is achieved by exploring new properties of the 1-D Routh canonical model and establishing new 2-D bilinear Routh canonical models. Without explicitly performing bilinear transformations, a computationally-efficient procedure is presented for finding the bilinear Routh reduced-order models. The properties of the obtained 2-D bilinear Routh approximants are discussed in detail. In addition, a new 2-D bilinear Routh canonical state-space realisation is presented from which the low-dimensional state-space models corresponding to the bilinear Routh approximants can be obtained by a direct truncation procedure. Furthermore, the relationships among the states of the bilinear Routh reduced-dimension model, the aggregated model, and the original system are explored. Numerical examples are given to demonstrate the effectiveness of the proposed method