Small Gain Theorem for Distributed Feedback Control of Sturm-Liouville Dynamics
Applied and Computational Mathematics
Volume 3, Issue 5, October 2014, Pages: 217-224
Received: Aug. 20, 2014; Accepted: Sep. 10, 2014; Published: Sep. 20, 2014
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Author
Boe-Shong Hong, Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62012, Taiwan
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Abstract
This paper constructs the small-gain theorem upon a general class of Sturm-Liouville systems. It appears that the feedback connection of two Sturm-Liouville sub-systems is guaranteed of well-posedness, Hurwitz, dissipativity and passivity in L2-spaces provided the loop gain is less than 1. To construct the theorem, spatiotemporal transfer-function and geometrical isomorphism between the space-time domain and the mode-frequency domain are developed, whereof the H∞-norm is extended to be 2D-H∞ norm in mode-frequency domain. On grounds of this small-gain theorem, robust performance of any Sturm-Liouville plant can be formulated as robust stability of a feedback connection, whereupon feedback syntheses can be performed via modal-spectral μ-loopshaping.
Keywords
Small Gain Theorem, Distributed Control, Robust Control, nD Transfer Function
To cite this article
Boe-Shong Hong, Small Gain Theorem for Distributed Feedback Control of Sturm-Liouville Dynamics, Applied and Computational Mathematics. Vol. 3, No. 5, 2014, pp. 217-224. doi: 10.11648/j.acm.20140305.14
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