<p>This study introduces a simplified and effective approach to Model Order Reduction (MOR) for large-scale linear dynamical systems, utilising an improved Singular Value Decomposition (ISVD) technique. The proposed ISVD improvements the standard Singular Value Decomposition (SVD) by introducing a dominancy-based criterion and improved balancing transformation, which retain system stability and steady-state accuracy while enhancing computing efficiency and the essential dynamic properties of the Higher-Order System (HOS). In order to solve this problem, the investigation presents a hybridized reduction framework that combines Singular Perturbation Approximation (SPA) and Balanced Truncation (BT) techniques, improved by a formulation based on improved SVD. By retaining the dominant system states and eliminating the less significant ones, the method ensures stability and maintains key behavioural traits of the original system. A known limitation of conventional Balanced Truncation (BT), specifically, the mismatch in steady-state gain, has been successfully addressed in this approach. The method incorporates the dominancy criteria. The method uses a simpler algorithm yet combines the best attributes of the SVD-based method. The effectiveness of the method is validated using several discrete-time Single-Input Single-Output (SISO) as well as Multi-Input Multi-Output (MIMO) systems and non-minimum phase system. The results are compared against existing techniques reported in the literature, demonstrating superior performance in terms of accuracy and efficiency.</p>

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Extended Improved SVD-Based Order Reduction for Discrete-Time Systems

  • Rishi Kumar,
  • Ashok Kumar Pandey,
  • Awadhesh Kumar

摘要

This study introduces a simplified and effective approach to Model Order Reduction (MOR) for large-scale linear dynamical systems, utilising an improved Singular Value Decomposition (ISVD) technique. The proposed ISVD improvements the standard Singular Value Decomposition (SVD) by introducing a dominancy-based criterion and improved balancing transformation, which retain system stability and steady-state accuracy while enhancing computing efficiency and the essential dynamic properties of the Higher-Order System (HOS). In order to solve this problem, the investigation presents a hybridized reduction framework that combines Singular Perturbation Approximation (SPA) and Balanced Truncation (BT) techniques, improved by a formulation based on improved SVD. By retaining the dominant system states and eliminating the less significant ones, the method ensures stability and maintains key behavioural traits of the original system. A known limitation of conventional Balanced Truncation (BT), specifically, the mismatch in steady-state gain, has been successfully addressed in this approach. The method incorporates the dominancy criteria. The method uses a simpler algorithm yet combines the best attributes of the SVD-based method. The effectiveness of the method is validated using several discrete-time Single-Input Single-Output (SISO) as well as Multi-Input Multi-Output (MIMO) systems and non-minimum phase system. The results are compared against existing techniques reported in the literature, demonstrating superior performance in terms of accuracy and efficiency.