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Development of stability-preserving time-limited model reduction framework for 2-D and 1-D models with error bound

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Abstract

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.

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Authors and Affiliations

  1. Department of Electrical Engineering, Military College of Signals, (MCS), National University of Sciences and Technology (NUST), Islamabad, 43000, Pakistan

    Muhammad Imran & Muhammad Imran

  2. Department of Electrical Engineering, Sir Syed (Center For Advanced Studies) Institute of Technology (SSCASE), Islamabad, 43000, Pakistan

    Syeda Hira Ambreen, Syed Nooh Hamdani & Muhammad Ejaz Naveed

  3. College of Science and Humanities, Rumah Majmaah University, Rumah, Kingdom of Saudi Arabia

    Maria Siddiqui

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  1. Muhammad Imran
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  2. Syeda Hira Ambreen
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  3. Syed Nooh Hamdani
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  4. Muhammad Imran
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  5. Muhammad Ejaz Naveed
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Correspondence to Muhammad Imran.

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M. Imran and S. H. Ambreen contributed equally to this work.

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Imran, M., Ambreen, S.H., Hamdani, S.N. et al. Development of stability-preserving time-limited model reduction framework for 2-D and 1-D models with error bound. Control Theory Technol. 20, 371–381 (2022). https://doi.org/10.1007/s11768-022-00109-8

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  • DOI: https://doi.org/10.1007/s11768-022-00109-8

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