Title :
Riesz Basis Property for Generic Network of Strings
Author :
Yanni, Guo ; Genqi, Xu ; Lingling, Yang
Author_Institution :
Acad. of Math. & Syst. Sci., Beijing
Abstract :
In this paper, we study the generation problem of Riesz basis for a generic network of strings with joint damping at all vertices. First we give spectral basic property of system operator A. Under certain conditions we prove that the spectrum of A distributes in a strip parallel to the imaginary axis. By the discussion of completeness of the generalized eigenvectors of operator A, we prove further that there exists a sequence of generalized eigenvectors of A that forms a Riesz basis with parentheses in the state Hilbert space.
Keywords :
Hilbert spaces; eigenvalues and eigenfunctions; graph theory; mathematical operators; network theory (graphs); sequences; Riesz basis property; generalized eigenvector; generic string network; graph theory; joint damping; sequences; spectral basic property; state Hilbert space; system operator; Controllability; Damping; Eigenvalues and eigenfunctions; Electronic mail; Equations; Flexible structures; Hilbert space; Mathematics; Stability; Strips; Riesz basis with parentheses; completeness; network; string equation;
Conference_Titel :
Control Conference, 2007. CCC 2007. Chinese
Conference_Location :
Hunan
Print_ISBN :
978-7-81124-055-9
Electronic_ISBN :
978-7-900719-22-5
DOI :
10.1109/CHICC.2006.4347543
