H∞ model reduction for discrete-time singular systems |
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Authors: | Shengyuan Xu James Lam |
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Affiliation: | a Center for Systems Engineering and Applied Mechanics (CESAME), Université Catholique de Louvain, Batiment Euler, Avenue G. Lemaître, 4, B-1348, Louvain-la-Neuve, Belgium;b Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong |
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Abstract: | This paper investigates the problem of H∞ model reduction for linear discrete-time singular systems. Without decomposing the original system matrices, necessary and sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. When these conditions are feasible, an explicit parametrization of the desired reduced-order models is given. Particularly, a simple LMI condition without rank constraint is derived for the zeroth-order H∞ approximation problem. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach. |
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Keywords: | Discrete-time systems H∞ model reduction Singular systems Linear matrix inequality |
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