Refined Eigenvalue Decay Bounds for Controllability Gramians of Sparsely-Actuated Symmetric LTI Systems

IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS IEEE Control Systems Letters Pub Date : 2025-01-16 DOI:10.1109/LCSYS.2025.3530636
Chenyan Zhu;Sandip Roy
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Abstract

Refined bounds are obtained for the eigenvalues of the controllability Gramian for a linear system with a Hurwitz, symmetric state matrix. The new bounds are phrased in terms of partial condition numbers (ratios of intermediate eigenvalues) of the state matrix. The bounds are found to compare favorably with existing results for several examples, particularly in cases where the system has time-scale separations or multiple eigenvalues in narrow bands.
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对于具有 Hurwitz 对称状态矩阵的线性系统,获得了可控性格拉米安特征值的改进边界。新的界限以状态矩阵的部分条件数(中间特征值的比率)来表述。在几个例子中,特别是在系统具有时间尺度分离或在窄带中具有多个特征值的情况下,发现这些边界与现有结果相比效果更佳。
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来源期刊
IEEE Control Systems Letters
IEEE Control Systems Letters Mathematics-Control and Optimization
CiteScore
4.40
自引率
13.30%
发文量
471
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