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EXPONENTIAL STABILITY OF INFINITE DIMENSIONAL LINEAR SYSTEMS
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 Title & Authors
EXPONENTIAL STABILITY OF INFINITE DIMENSIONAL LINEAR SYSTEMS
Shin, Chang Eon;
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 Abstract
In this paper, we show that if is a differential subalgebra of Banach algebras , , then solutions of the infinite dimensional linear system associated with a matrix in have its p-exponential stability being equivalent to each other for different .
 Keywords
infinite matrix;differential subalgebra;Lyapunov equation;linear system;exponential stability;
 Language
English
 Cited by
 References
1.
R. F. Curtain and H. J. Zwart, An Introduction to Infinite Dimensional Linear Systems Theorey, Springer-Verlag, New York, 1995.

2.
K. Grochenig, Wiener's lemma: theme and variations, an introduction to spectral invariance and its applications, In Four Short Courses on Harmonic Analysis: Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis, edited by P. Massopust and B. Forster, Birkhauser, Boston 2010.

3.
K. Grochenig and A. Klotz, Noncommutative approximation: inverse-closed subalgebras and off-diagonal decay of matrices, Constr. Approx. 32 (2010), no. 3, 429-466. crossref(new window)

4.
K. Grochenig and M. Leinert, Symmetry and inverse-closedness of matrix algebras and functional calculus for infinite matrices, Trans. Amer. Math. Soc. 358 (2006), 2695-2711. crossref(new window)

5.
M. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Alge-bra, Academic Press, San Diego, 1974.

6.
I. Krishtal, Wiener's lemma: pictures at exhibition, Rev. Un. Mat. Argentina 52 (2011), no. 2, 61-79.

7.
N. Motee and A. Jadbabie, Optimal control of spatially distributed systems, IEEE Trans. Automat. Control 53 (2008), no. 7, 1616-1629. crossref(new window)

8.
N. Motee and Q. Sun, Sparsity measures for spatially decaying systems, arXiv:1402.4148.

9.
C. E. Shin, Infinite matrices with subpolynomial off-diagonal decay, in preparation.

10.
C. E. Shin and Q. Sun, Wiener's lemma: localization and various approaches, Appl. Math. J. Chinese Univ. Ser. B 28 (2013), no. 4, 465-484. crossref(new window)

11.
Q. Sun, Wiener's lemma for infinite matrices with polynomial off-diagonal decay, C. R. Math. Acad. Sci. Paris 340 (2005), no. 8, 567-570. crossref(new window)

12.
Q. Sun, Wiener's lemma for infinite matrices, Trans. Amer. Math. Soc. 359 (2007), no. 7, 3099-3123. crossref(new window)

13.
Q. Sun, Wiener's lemma for infinite matrices II, Constr. Approx. 34 (2011), no. 2, 209-235. crossref(new window)