Model Reduction for Discrete-Time Systems via Optimization over Grassmann Manifold

Yiqin Lin and Liping Zhou ()
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Yiqin Lin: School of Science, Hunan University of Science and Engineering, Yongzhou 425199, China
Liping Zhou: School of Science, Hunan University of Science and Engineering, Yongzhou 425199, China

Mathematics, 2025, vol. 13, issue 17, 1-23

Abstract: In this paper, we investigate h 2 -optimal model reduction methods for discrete-time linear time-invariant systems. Similar to the continuous-time case, we will formulate this problem as an optimization problem over a Grassmann manifold. We consider constructing reduced systems by both one-sided and two-sided projections. For one-sided projection, by utilizing the principle of the Grassmann manifold, we propose a gradient flow method and a sequentially quadratic approximation approach to solve the optimization problem. For two-sided projection, we apply the strategies of alternating direction iteration and sequentially quadratic approximation to the minimization problem and develop a numerically efficient method. One main advantage of these methods, based on the formulation of optimization over a Grassmann manifold, is that stability can be preserved in the reduced system. Several numerical examples are provided to illustrate the effectiveness of the methods proposed in this paper.

Keywords: discrete-time system; model reduction; Grassmann manifold; optimization; h 2 approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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