Reduced-order state-space models for two-dimensional discrete systems via bivariate discrete orthogonal polynomials

This paper investigates the new model order reduction (MOR) methods via bivariate discrete orthogonal polynomials for two-dimensional (2-D) discrete systems. The 2-D discrete system is described by the Kurek model. First, we deduce algebraically the shift-transformation matrix of the classical discrete orthogonal polynomials of one variable. By means of the shift-transformation matrices, 2-D discrete systems are expanded in the spaces spanned by bivariate discrete orthogonal polynomials. The coefficient matrices are calculated from matrix equations. Then the reduced-order systems are produced by the orthogonal projection matrices defined by the coefficient matrices. Theoretical analysis shows that the reduced-order systems can match a certain number of coefficient vectors of the original outputs. Finally, one numerical example is simulated to demonstrate the feasibility and effectiveness of the proposed methods.