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Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems
On asymptotically autonomous dynamics for multivalued evolution problems
Instituto de Matemática e Computação, Universidade Federal de Itajubá, 37500-903 - Itajubá - Minas Gerais, Brazil |
In this work we improve the result presented by Kloeden-Simsen-Stefanello Simsen in [
References:
[1] |
J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984.
doi: 10.1007/978-3-642-69512-4. |
[2] |
T. Caraballo, P. E. Kloeden and P. Marín-Rubio,
Weak pullback attractors of setvalued processes, J. Math. Anal. Appl., 288 (2003), 692-707.
doi: 10.1016/j.jmaa.2003.09.039. |
[3] |
T. Caraballo, J. A. Langa, V. S. Melnik and J. Valero,
Pullback attractors for nonautonomous and stochastic multivalued dynamical systems, Set-Valued Analysis, 11 (2003), 153-201.
doi: 10.1023/A:1022902802385. |
[4] |
T. Caraballo, P. Marin-Rubio and J. C. Robinson,
A comparison between two theories for multivalued semiflows and their asymptotic behaviour, Set-Valued Analysis, 11 (2003), 297-322.
doi: 10.1023/A:1024422619616. |
[5] |
J. I. Díaz and I. I. Vrabie,
Existence for reaction diffusion systems. A compactness method approach, J. Math. Anal. Appl., 188 (1994), 521-540.
doi: 10.1006/jmaa.1994.1443. |
[6] |
P. E. Kloeden and J. Simsen,
Pullback attractors for non-autonomous evolution equations with spatially variable exponents, Communications on Pure and Applied Analysis, 13 (2014), 2543-2557.
doi: 10.3934/cpaa.2014.13.2543. |
[7] |
P. E. Kloeden and J. Simsen,
Attractors of asymptotically autonomous quasilinear parabolic equation with spatially variable exponents, J. Math. Anal. Appl., 425 (2015), 911-918.
doi: 10.1016/j.jmaa.2014.12.069. |
[8] |
P. E. Kloeden, J. Simsen and M. S. Simsen,
Asymptotically autonomous multivalued Cauchy problems with spatially variable exponents, J. Math. Anal. Appl., 445 (2017), 513-531.
doi: 10.1016/j.jmaa.2016.08.004. |
[9] |
Y. Li, L. She and R. Wang,
Asymptotically autonomous dynamics for parabolic equations, J. Math. Anal. Appl., 459 (2018), 1106-1123.
doi: 10.1016/j.jmaa.2017.11.033. |
[10] |
V. S. Melnik and J. Valero,
On attractors of multivalued semi-flows and differential inclusions, Set-Valued Anal., 6 (1998), 83-111.
doi: 10.1023/A:1008608431399. |
[11] |
V. S. Melnik and J. Valero,
On global attractors of multivalued semiprocesses and nonautonomous evolution inclusions, Set-Valued Analysis, 8 (2000), 375-403.
doi: 10.1023/A:1026514727329. |
[12] |
N. S. Papageorgiou and F. Papalini,
On the structure of the solution set of evolution inclusions with time-dependent subdifferentials, Rend. Sem. Mat. Univ. Padova, 97 (1997), 163-186.
|
[13] |
J. Simsen and E. Capelato, Some properties for exact generalized processes. Continuous and distributed systems. Ⅱ, 209-219, Stud. Syst. Decis. Control, 30, Springer, Cham, 2015.
doi: 10.1007/978-3-319-19075-4_12. |
[14] |
J. Simsen and C. B. Gentile,
On attractors for multivalued semigroups defined by generalized semiflows, Set-Valued Anal., 16 (2008), 105-124.
doi: 10.1007/s11228-006-0037-1. |
show all references
References:
[1] |
J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984.
doi: 10.1007/978-3-642-69512-4. |
[2] |
T. Caraballo, P. E. Kloeden and P. Marín-Rubio,
Weak pullback attractors of setvalued processes, J. Math. Anal. Appl., 288 (2003), 692-707.
doi: 10.1016/j.jmaa.2003.09.039. |
[3] |
T. Caraballo, J. A. Langa, V. S. Melnik and J. Valero,
Pullback attractors for nonautonomous and stochastic multivalued dynamical systems, Set-Valued Analysis, 11 (2003), 153-201.
doi: 10.1023/A:1022902802385. |
[4] |
T. Caraballo, P. Marin-Rubio and J. C. Robinson,
A comparison between two theories for multivalued semiflows and their asymptotic behaviour, Set-Valued Analysis, 11 (2003), 297-322.
doi: 10.1023/A:1024422619616. |
[5] |
J. I. Díaz and I. I. Vrabie,
Existence for reaction diffusion systems. A compactness method approach, J. Math. Anal. Appl., 188 (1994), 521-540.
doi: 10.1006/jmaa.1994.1443. |
[6] |
P. E. Kloeden and J. Simsen,
Pullback attractors for non-autonomous evolution equations with spatially variable exponents, Communications on Pure and Applied Analysis, 13 (2014), 2543-2557.
doi: 10.3934/cpaa.2014.13.2543. |
[7] |
P. E. Kloeden and J. Simsen,
Attractors of asymptotically autonomous quasilinear parabolic equation with spatially variable exponents, J. Math. Anal. Appl., 425 (2015), 911-918.
doi: 10.1016/j.jmaa.2014.12.069. |
[8] |
P. E. Kloeden, J. Simsen and M. S. Simsen,
Asymptotically autonomous multivalued Cauchy problems with spatially variable exponents, J. Math. Anal. Appl., 445 (2017), 513-531.
doi: 10.1016/j.jmaa.2016.08.004. |
[9] |
Y. Li, L. She and R. Wang,
Asymptotically autonomous dynamics for parabolic equations, J. Math. Anal. Appl., 459 (2018), 1106-1123.
doi: 10.1016/j.jmaa.2017.11.033. |
[10] |
V. S. Melnik and J. Valero,
On attractors of multivalued semi-flows and differential inclusions, Set-Valued Anal., 6 (1998), 83-111.
doi: 10.1023/A:1008608431399. |
[11] |
V. S. Melnik and J. Valero,
On global attractors of multivalued semiprocesses and nonautonomous evolution inclusions, Set-Valued Analysis, 8 (2000), 375-403.
doi: 10.1023/A:1026514727329. |
[12] |
N. S. Papageorgiou and F. Papalini,
On the structure of the solution set of evolution inclusions with time-dependent subdifferentials, Rend. Sem. Mat. Univ. Padova, 97 (1997), 163-186.
|
[13] |
J. Simsen and E. Capelato, Some properties for exact generalized processes. Continuous and distributed systems. Ⅱ, 209-219, Stud. Syst. Decis. Control, 30, Springer, Cham, 2015.
doi: 10.1007/978-3-319-19075-4_12. |
[14] |
J. Simsen and C. B. Gentile,
On attractors for multivalued semigroups defined by generalized semiflows, Set-Valued Anal., 16 (2008), 105-124.
doi: 10.1007/s11228-006-0037-1. |
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