Premium
Stabilization and SDG condition of serially connected vibrating strings system with discontinuous displacement
Author(s) -
Han ZhongJie,
Xu GenQi
Publication year - 2012
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.218
Subject(s) - displacement (psychology) , eigenvalues and eigenvectors , state (computer science) , basis (linear algebra) , mathematics , control theory (sociology) , sequence (biology) , transversal (combinatorics) , connection (principal bundle) , mathematical analysis , topology (electrical circuits) , pure mathematics , control (management) , computer science , physics , combinatorics , geometry , algorithm , artificial intelligence , psychology , quantum mechanics , biology , psychotherapist , genetics
AbstractBased on joint feedback controls, the stabilization issue of a serially connected vibrating strings system is presented. Suppose that the two ends of the strings system are clamped and the vertical force of strings is continuous at interior nodes while the transversal displacement is discontinuous. The vertical force of strings at interior nodes are observed and the compensators are derived from the observation values. Then the feedback controllers are arranged at interior nodes to stabilize this system. Through a detailed spectral analysis, this closed loop system is proved to be asymptotically stable and there exists a sequence of (generalized) eigenvectors of the system that forms a Riesz basis with parentheses for the state space under certain conditions. Hence the spectrum‐determined‐growth (SDG) condition holds. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society