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Two-dimensional models are challenging to deal with because of their complex structure. As the model's order grows larger, simulation, analysis, design, and control become more challenging. For one-dimensional and two-dimensional models, Enns' weighted (i.e. frequency and time) model reduction procedures result in an unstable reduced-order model. For one-dimensional reduced-order systems, researchers devised a number of frequency-weighted stability-preserving solutions; nevertheless, these solutions result in significant approximation errors. However, to the best of the authors' knowledge, no time-weighted stability-preserving model reduction framework is available in the literature for the discrete-time one-dimensional and two-dimensional systems. In this research, two-dimensional models are separated into two sub-models (i.e. two cascaded one-dimensional models) and reduced using time-weighted Gramians utilising minimal rank-decomposition. The approach applies to both one-dimensional and two-dimensional models. For one-dimensional and two-dimensional models, the suggested methodology additionally gives  a priori  error-bounds expressions. Numerical results and comparisons to existing methodologies illustrate the efficacy of the proposed methodology.

Model order reduction framework for discrete-time systems with error bound via balanced structure