Due to their complex structure, 2-D models are challenging to work with;additionally, simulation, analysis, design, and control get increasingly difficult as the order of the model grows. Moreover, in particular time intervals, Gawronski and Juang's time-limited model reduction schemes produce an unstable reduced-order model for the 2-D and 1-D models. Researchers revealed some stability preservation solutions to address this key flaw which ensure the stability of 1-D reduced-order systems;nevertheless, these strategies result in large approximation errors. However, to the best of the authors' knowledge, there is no literature available for the stability preserving time-limited-interval Gramian-based model reduction framework for the 2-D discrete-time systems. In this article, 2-D models are decomposed into two separate sub-models (i.e., two cascaded 1-D models) using the condition of minimal rank-decomposition. Model reduction procedures are conducted on these obtained two 1-D sub-models using limited-time Gramian. The suggested methodology works for both 2-D and 1-D models. Moreover, the suggested methodology gives the stability of the reduced model as well as a priori error-bound expressions for the 2-D and 1-D models. Numerical results and comparisons between existing and suggested methodologies are provided to demonstrate the effectiveness of the suggested methodology.

Muhammad Imran;Syeda Hira Ambreen;Syed Nooh Hamdani;Muhammad Ejaz Naveed;Maria Siddiqui

Department of Electrical Engineering,Military College of Signals,(MCS),National University of Sciences and Technology(NUST),Islamabad 43000,Pakistan;Department of Electrical Engineering, Sir Syed (Center ForAdvanced Studies) Institute of Technology (SSCASE),Islamabad 43000, Pakistan;College of Science and Humanities, Rumah MajmaahUniversity, Rumah, Kingdom of Saudi Arabia

控制理论与技术（英文版）

[1]Muhammad Imran;Syeda Hira Ambreen;Syed Nooh Hamdani;Muhammad Ejaz Naveed;Maria Siddiqui-.Development of stability-preserving time-limited model reduction framework for 2-D and 1-D models with error bound)[J].控制理论与技术（英文版）,2022(03):371-381

Gawronski,Juang

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