Abstract
AbstractIn this paper, we describe a linear boundary non‐collocated feedback controller to stabilize a string system with variable coefficients and investigate the exponential stability of the closed‐loop system. We show that the system associates with a C0 semigroup. Through the asymptotic analysis technique, we get the asymptotic values of all eigenvalues of the system operator 𝒜. Furthermore, we prove that there is a sequence of generalized eigenvectors of 𝒜 that forms a Riesz basis with parentheses for the energy state space. Hence, the system satisfies the spectrum determined growth assumption. Finally, we show that the system is exponentially stable with suitable choice of the feedback gains.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.