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Almost periodic solutions for a weakly dissipated hybrid system
Algebraic characterization of autonomy and controllability of behaviours of spatially invariant systems
1. | Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE |
References:
[1] |
J. A. Ball and O. J. Staffans, Conservative state-space realizations of dissipative system behaviors, Integral Equations Operator Theory, 54 (2006), 151-213.
doi: 10.1007/s00020-003-1356-3. |
[2] |
Madhu Belur, Control in a Behavioral Context, Ph.D Thesis, Rijksuniversiteit Groningen, The Netherlands, 2003. Available from: http://www.dissertations.ub.rug.nl/faculties/science/2003/m.n.belur/. |
[3] |
R. W. Carroll, Abstract Methods in Partial Differential Equations, Harper's Series in Modern Mathematics, Harper & Row, New York-London, 1969. |
[4] |
R. F. Curtain, O. V. Iftime and H. J. Zwart, System theoretic properties of a class of spatially invariant systems, Automatica J. IFAC, 45 (2009), 1619-1627.
doi: 10.1016/j.automatica.2009.03.005. |
[5] |
R. F. Curtain and A. J. Sasane, On Riccati equations in Banach algebras, SIAM J. Control Optim., 49 (2011), 464-475.
doi: 10.1137/100806011. |
[6] |
W. F. Donoghue, Jr., Distributions and Fourier Transforms, Pure and Applied Mathematics, 32, Academic Press, New York-London, 1969. |
[7] |
L. Hörmander, Null solutions of partial differential equations, Arch. Rational Mech. Anal., 4 (1960), 255-261. |
[8] |
L. Hörmander, The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis, 2nd edition, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 256, Springer-Verlag, Berlin, 1990. |
[9] |
U. Oberst and M. Scheicher, Time-autonomy and time-controllability of discrete multidimensional behaviors, Internat. J. Control, 85 (2012), 990-1009.
doi: 10.1080/00207179.2012.673135. |
[10] |
J. W. Polderman and J. C. Willems, Introduction to Mathematical Systems Theory. A Behavioral Approach, Texts in Applied Mathematics, 26, Springer-Verlag, New York, 1998. |
[11] |
H. K. Pillai and S. Shankar, A behavioral approach to control of distributed systems, SIAM J. Control Optim., 37 (1999), 388-408.
doi: 10.1137/S0363012997321784. |
[12] |
A. J. Sasane, E. G. F. Thomas and J. C. Willems, Time-autonomy versus time-controllability, Systems Control Lett., 45 (2002), 145-153.
doi: 10.1016/S0167-6911(01)00174-8. |
show all references
References:
[1] |
J. A. Ball and O. J. Staffans, Conservative state-space realizations of dissipative system behaviors, Integral Equations Operator Theory, 54 (2006), 151-213.
doi: 10.1007/s00020-003-1356-3. |
[2] |
Madhu Belur, Control in a Behavioral Context, Ph.D Thesis, Rijksuniversiteit Groningen, The Netherlands, 2003. Available from: http://www.dissertations.ub.rug.nl/faculties/science/2003/m.n.belur/. |
[3] |
R. W. Carroll, Abstract Methods in Partial Differential Equations, Harper's Series in Modern Mathematics, Harper & Row, New York-London, 1969. |
[4] |
R. F. Curtain, O. V. Iftime and H. J. Zwart, System theoretic properties of a class of spatially invariant systems, Automatica J. IFAC, 45 (2009), 1619-1627.
doi: 10.1016/j.automatica.2009.03.005. |
[5] |
R. F. Curtain and A. J. Sasane, On Riccati equations in Banach algebras, SIAM J. Control Optim., 49 (2011), 464-475.
doi: 10.1137/100806011. |
[6] |
W. F. Donoghue, Jr., Distributions and Fourier Transforms, Pure and Applied Mathematics, 32, Academic Press, New York-London, 1969. |
[7] |
L. Hörmander, Null solutions of partial differential equations, Arch. Rational Mech. Anal., 4 (1960), 255-261. |
[8] |
L. Hörmander, The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis, 2nd edition, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 256, Springer-Verlag, Berlin, 1990. |
[9] |
U. Oberst and M. Scheicher, Time-autonomy and time-controllability of discrete multidimensional behaviors, Internat. J. Control, 85 (2012), 990-1009.
doi: 10.1080/00207179.2012.673135. |
[10] |
J. W. Polderman and J. C. Willems, Introduction to Mathematical Systems Theory. A Behavioral Approach, Texts in Applied Mathematics, 26, Springer-Verlag, New York, 1998. |
[11] |
H. K. Pillai and S. Shankar, A behavioral approach to control of distributed systems, SIAM J. Control Optim., 37 (1999), 388-408.
doi: 10.1137/S0363012997321784. |
[12] |
A. J. Sasane, E. G. F. Thomas and J. C. Willems, Time-autonomy versus time-controllability, Systems Control Lett., 45 (2002), 145-153.
doi: 10.1016/S0167-6911(01)00174-8. |
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