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Approximate controllability of discrete semilinear systems and applications
1. | Louisiana State University, Department of Mathematics, Baton Rouge, LA 70803, United States |
2. | Universidad de Los Andes, Facualtad de Ciencias, Departamento de Matematica, Merida, 5101, Venezuela |
References:
[1] |
A. E. Bashirov and K. R. Kerimov, On controllability conception for stochastic systems, SIAM Journal on Control and Optimization, 35 (1997), 384-398.
doi: 10.1137/S0363012994260970. |
[2] |
A. E. Bashirov and N. I. Mahmudov, On Controllability of deterministic and stochastic systems, SIAM Journal on Control and Optimization, 37 (1999), 1808-1821.
doi: 10.1137/S036301299732184X. |
[3] |
A. E. Bashirov, N. Mahmudov, N. Semi and H. Etikan, Partial controllability concepts, Iternational Journal of Control, 80 (2007), 1-7.
doi: 10.1080/00207170600885489. |
[4] |
A. E. Bashirov and N. I. Mahmudov, Partial controllability of stochastic linear systems, International Journal of Control, 83 (2010), 2564-2572.
doi: 10.1080/00207179.2010.532570. |
[5] |
A. E. Bashirov and N. Ghahramanlou, On Partial approximate controllability of semilinear systems, Cogent Engineering, 1 (2014), 965947.
doi: 10.1080/23311916.2014.965947. |
[6] |
A. E. Bashirov and N. Ghahramanlou, On Partial S-controllability of semilinear partially observable Systems, International Journal of Control, 88 (2015), 969-982.
doi: 10.1080/00207179.2014.986763. |
[7] |
R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems, Lecture Notes in Control and Information Sciences, 8, (1978), Springer Verlag, Berlin. |
[8] |
R. F. Curtain and H. J. Zwart, An Introduction to Infinite Dimensional Linear Systems Theory, Text in Applied Mathematics, 21 (1995), Springer Verlag, New York.
doi: 10.1007/978-1-4612-4224-6. |
[9] |
S. N. Chow and H. Leiva, Existence and roughness of the exponential dichotomy for linear skew-product semiflows in Banach spaces, J. Differential Equations, 120 (1995), 429-477.
doi: 10.1006/jdeq.1995.1117. |
[10] |
D. Henry, Geometry Theory of Semilinear Parabolic Equations, Lectures Notes in Mathematics, 840 (1981) Springer Verlag, Berlin. |
[11] |
H. R. Henriquez and C. Cuevas, Approximate controllability of abstract discrete-time systems, Advances in Difference Equations,840 (2010), Article ID 695290, 17 pages.
doi: 10.1155/2010/695290. |
[12] |
V. Lakshmikanthan and D. Trigiante, Theory of Difference Equations: Numerical Methods and Applications, Mathematics in Science and Engineering, 1998. |
[13] |
H. Leiva, A Lemma on $C_{0}$-semigroups and applications PDEs systems, Quaestions Mathematicae, 26 (2003), 247-265.
doi: 10.2989/16073600309486057. |
[14] |
H. Leiva and J. Uzcategui, Exact controlllability for semilinear difference equation and application J. Difference Equ. Appl.,14 (2008), 671-679.
doi: 10.1080/10236190701726170. |
[15] |
H. Leiva and J. Uzcategui, Controllability of linear difference equations in Hilbert Spaces and applications, IMA Journal of Math. Control and Information, 25 (2008), 323-340.
doi: 10.1093/imamci/dnm027. |
[16] |
H. Leiva and J. Uzcátegui, Approximate controllability of semilinear difference equations and applications, Journal Mathematical Control Science and Applications (JMCSA), 4 (2011), 9-19. |
[17] |
M. Megan, A. L. Sasu and B. Sasu, On approximate controllability of systems associated to linear skew product semiflows, Analele Univ. I. Cuza, Iasi, 47 (2001), 379-388. |
[18] |
M. Megan, A. L. Sasu and B. Sasu, Stabilizability and controllability of systems associated to linear skew product semiflows, Rev. Mat. Complut., 15 (2002), 599-618.
doi: 10.5209/rev_REMA.2002.v15.n2.16932. |
[19] |
A. L. Sasu and B. Sasu, Stability and stabilizability for linear systems of difference equations, J. Difference Equ. Appl., 10 (2004), 1085-1105.
doi: 10.1080/10236190412331314178. |
[20] |
A. L. Sasu, Stabilizability and controllability for systems of difference equations, J. Difference Equ. Appl.,12 (2006), 821-826.
doi: 10.1080/10236190600734218. |
show all references
References:
[1] |
A. E. Bashirov and K. R. Kerimov, On controllability conception for stochastic systems, SIAM Journal on Control and Optimization, 35 (1997), 384-398.
doi: 10.1137/S0363012994260970. |
[2] |
A. E. Bashirov and N. I. Mahmudov, On Controllability of deterministic and stochastic systems, SIAM Journal on Control and Optimization, 37 (1999), 1808-1821.
doi: 10.1137/S036301299732184X. |
[3] |
A. E. Bashirov, N. Mahmudov, N. Semi and H. Etikan, Partial controllability concepts, Iternational Journal of Control, 80 (2007), 1-7.
doi: 10.1080/00207170600885489. |
[4] |
A. E. Bashirov and N. I. Mahmudov, Partial controllability of stochastic linear systems, International Journal of Control, 83 (2010), 2564-2572.
doi: 10.1080/00207179.2010.532570. |
[5] |
A. E. Bashirov and N. Ghahramanlou, On Partial approximate controllability of semilinear systems, Cogent Engineering, 1 (2014), 965947.
doi: 10.1080/23311916.2014.965947. |
[6] |
A. E. Bashirov and N. Ghahramanlou, On Partial S-controllability of semilinear partially observable Systems, International Journal of Control, 88 (2015), 969-982.
doi: 10.1080/00207179.2014.986763. |
[7] |
R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems, Lecture Notes in Control and Information Sciences, 8, (1978), Springer Verlag, Berlin. |
[8] |
R. F. Curtain and H. J. Zwart, An Introduction to Infinite Dimensional Linear Systems Theory, Text in Applied Mathematics, 21 (1995), Springer Verlag, New York.
doi: 10.1007/978-1-4612-4224-6. |
[9] |
S. N. Chow and H. Leiva, Existence and roughness of the exponential dichotomy for linear skew-product semiflows in Banach spaces, J. Differential Equations, 120 (1995), 429-477.
doi: 10.1006/jdeq.1995.1117. |
[10] |
D. Henry, Geometry Theory of Semilinear Parabolic Equations, Lectures Notes in Mathematics, 840 (1981) Springer Verlag, Berlin. |
[11] |
H. R. Henriquez and C. Cuevas, Approximate controllability of abstract discrete-time systems, Advances in Difference Equations,840 (2010), Article ID 695290, 17 pages.
doi: 10.1155/2010/695290. |
[12] |
V. Lakshmikanthan and D. Trigiante, Theory of Difference Equations: Numerical Methods and Applications, Mathematics in Science and Engineering, 1998. |
[13] |
H. Leiva, A Lemma on $C_{0}$-semigroups and applications PDEs systems, Quaestions Mathematicae, 26 (2003), 247-265.
doi: 10.2989/16073600309486057. |
[14] |
H. Leiva and J. Uzcategui, Exact controlllability for semilinear difference equation and application J. Difference Equ. Appl.,14 (2008), 671-679.
doi: 10.1080/10236190701726170. |
[15] |
H. Leiva and J. Uzcategui, Controllability of linear difference equations in Hilbert Spaces and applications, IMA Journal of Math. Control and Information, 25 (2008), 323-340.
doi: 10.1093/imamci/dnm027. |
[16] |
H. Leiva and J. Uzcátegui, Approximate controllability of semilinear difference equations and applications, Journal Mathematical Control Science and Applications (JMCSA), 4 (2011), 9-19. |
[17] |
M. Megan, A. L. Sasu and B. Sasu, On approximate controllability of systems associated to linear skew product semiflows, Analele Univ. I. Cuza, Iasi, 47 (2001), 379-388. |
[18] |
M. Megan, A. L. Sasu and B. Sasu, Stabilizability and controllability of systems associated to linear skew product semiflows, Rev. Mat. Complut., 15 (2002), 599-618.
doi: 10.5209/rev_REMA.2002.v15.n2.16932. |
[19] |
A. L. Sasu and B. Sasu, Stability and stabilizability for linear systems of difference equations, J. Difference Equ. Appl., 10 (2004), 1085-1105.
doi: 10.1080/10236190412331314178. |
[20] |
A. L. Sasu, Stabilizability and controllability for systems of difference equations, J. Difference Equ. Appl.,12 (2006), 821-826.
doi: 10.1080/10236190600734218. |
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