A lower bound for the stability radius of time-varying systems

Proceedings of the American Mathematical Society

Volumn 132, Issue 12, 2004, Pages 3653-3659

  Sasu, Adina Luminiţa ^a   Sasu, Bogdan ^a  

^a WEST UNIVERSITY OF TIMISOARA   (Romania)

Author keywords

Linear skew product semiflows; Stability radius

Indexed keywords

EID: 10144234802     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-04-07513-6     Document Type: Conference Paper

References (20)

1. J. A. Ball, I. Gohberg, and M. A. Kaashoek, Two-sided Nudelman interpolation for input-output operators of discrete time-varying systems, Integral Equations Operator Theory 21 (1995), 174-211. MR 95m:47018
2. J. A. Ball, I. Gohberg, and M. A. Kaashoek, Input-output operators of J-unitary time-varying continuous time systems, Oper. Theory Adv. Appl. 75 (1995), 57-94. MR 96c:47109
3. J. A. Ball, I. Gohberg, and M. A. Kaashoek, A frequency response function for linear, time-varying systems, Math. Control Signals Systems 8 (1995), 334-351. MR 97h:93014
4. C. Chicone and Y. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, Mathematical Surveys and Monographs, vol. 70, Amer. Math. Soc., Providence, RI, 1999. MR 2001e:47068
5. S.-N. Chow and H. Leiva, Existence and roughness of the exponential dichotomy for linear skew-product semiflows in Banach space, J. Differential Equations 120 (1995), 429-477. MR 97a:34121
6. S.-N. Chow and H. Leiva, Unbounded perturbation of the exponential dichotomy for evolution equations, J. Differential Equations 129 (1996), 509-531. MR 98d:34090
7. S. Clark, Y. Latushkin, S. Montgomery-Smith, and T. Randolph, Stability radius and internal versus external stability in Banach spaces: an evolution semigroup approach, SIAM J. Control Optimization 38 (2000), 1757-1793. MR 2001k:93085
8. D. Hinrichsen, A. Ilchmann, and A. J. Pritchard, Robustness of stability of time-varying linear systems, J. Differential Equations 82 (1989), 219-250. MR 91b:93122
9. D. Hinrichsen and A. J. Pritchard, Robust stability of linear operators on Banach spaces, SIAM J. Control Optim. 32 (1994), 1503-1541. MR 95i:93109
10. Y. Latushkin, S. Montgomery-Smith, and T. Randolph, Evolutionary semigroups and dichotomy of linear skew-product flows on spaces with Banach fibers, J. Differential Equations 125 (1996), 73-116. MR 97a:47056
11. Y. Latushkin and R. Schnaubelt, Evolution semigroups, translation algebras and exponential dichotomy of cocycles, J. Differential Equations 159 (1999), 321-369. MR 2000k:47054
12. M. Megan, B. Sasu, and A. L. Sasu, On nonuniform exponential dichotomy of evolution operators in Banach spaces, Integral Equations Operator Theory 44 (2002), 71-78. MR 2003d:47058
13. M. Megan, A. L. Sasu, and B. Sasu, Discrete admissibility and exponential dichotomy for evolution families, Discrete Contin. Dynam. Systems 9 (2003), 383-397. MR 2003k:47054
14. M. Megan, A. L. Sasu, and B. Sasu, Stabilizability and controllability of systems associated to linear skew-product semiflows, Rev. Mat. Complutense 15 (2002), 599-618. MR 2004b:93114
15. M. Megan, A. L. Sasu, and B. Sasu, Theorems of Perron type for uniform exponential dichotomy of linear skew-product semiflows, Bull. Belg. Math. Soc. Simon Stevin 10 (2003), 1-21.
16. M. Megan, A. L. Sasu, and B. Sasu, Perron conditions for uniform exponential expansiveness of linear skew-product flows, Monatsh. Math. 138 (2003), 145-157. MR 2003k:47055
17. M. Megan, A. L. Sasu, and B. Sasu, Perron conditions for pointwise and global exponential dichotomy of linear skew-product flows, accepted for publication in Integral Equations Operator Theory.
18. M. Megan, A. L. Sasu, and B. Sasu, Uniform exponential dichotomy and admissibility for linear skew-product semiflows, Oper. Theory Adv. Appl. (2003).
19. M. Megan, A. L. Sasu, and B. Sasu, Theorems of Perron type for uniform exponential stability of linear skew-product semiflows, accepted for publication in Dynam. Contin. Discrete Impuls. Systems.
20. R. J. Sacker and G. R. Sell, Dichotomies for linear evolutionary equations in Banach spaces, J. Differential Equations 113 (1994), 17-67. MR 96k:34136