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Clarke directional derivatives of regularized gap functions for nonsmooth quasi-variational inequalities
Approximations of infinite dimensional disturbance decoupling and almost disturbance decoupling problems
1. | Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China |
References:
[1] |
J. H. Bramble and V. Thomée, Discrete time Galerkin methods for a parabolic boundary value problem, Ann. Mat. Pura Appl., 101 (1974), 115-152.
doi: 10.1007/BF02417101. |
[2] |
R. F. Curtain, Disturbance decoupling by measurement feedback with stability for infinite dimensional systems, Internat. J. Control, 43 (1986), 1723-1743.
doi: 10.1080/00207178608933569. |
[3] |
R. F. Curtain, Invariance concepts in infinite dimensions, SIAM J. Control Optim., 24 (1986), 1009-1031.
doi: 10.1137/0324059. |
[4] |
R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems Theory, Lecture Notes in Control and Information Sciences, 8, Springer-Verlag, Berlin, 1978. |
[5] |
R. E. Edwards, Fourier Series, a Modern Introduction, vol.II, $2^{nd}$ edition, Springer-Verlag, New York, 1982. |
[6] |
L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, vol. 19, American Mathematical Society, 1998. |
[7] |
K. A. Morris and R. Rebarber, Feedback invariance of SISO infinite dimensional systems, Math. Control Signals Systems, 19 (2007), 311-335.
doi: 10.1007/s00498-007-0021-9. |
[8] |
L. Pandolfi, Disturbance decoupling and invariant subspaces for delay systems, Appl. Math. Optim., 14 (1986), 55-72.
doi: 10.1007/BF01442228. |
[9] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[10] |
E. J. P. G. Schmidt and R. J. Stern, Invariance theory for infinite dimensional linear control systems, Appl. Math. Optim., 6 (1980), 113-122.
doi: 10.1007/BF01442887. |
[11] |
J. M. Schumacher, A direct approach to compensator design for distributed parameter systems, SIAM J. Control Optim., 21 (1983), 823-836.
doi: 10.1137/0321050. |
[12] |
H. L. Trentelman, Almost Invariant Subspaces and High Gain Feedback, Ph.D thesis, Rijksuniversiteit Groningen, 1986. |
[13] |
J. C. Willems, Almost invariant subspaces: An approach to high gain feedback design-part I: Almost controlled invariant subspaces, IEEE Trans. Automat. Control, 26 (1981), 235-252.
doi: 10.1109/TAC.1981.1102551. |
[14] |
J. L. Willems, Disturbance isolation in linear feedback systems, Int. J. Syst. Sci., 6 (1975), 233-238.
doi: 10.1080/00207727508941812. |
[15] |
W. M. Wonham, Linear Multivariable Control: A Geometric Approach, $2^{nd}$ edition, Springer-Verlag, New York, 1979. |
[16] |
H. J. Zwart, Geometric Theory for Infinite Dimensional Systems, Lecture Notes in Control and Information Sciences, 115, Springer-Verlag, Berlin, 1989.
doi: 10.1007/BFb0044353. |
[17] |
H. J. Zwart, Equivalence between open-loop and closed-loop invariance for infinite-dimensional systems: a frequency domain approach, SIAM J. Control Optim., 26 (1988), 1175-1199.
doi: 10.1137/0326065. |
show all references
References:
[1] |
J. H. Bramble and V. Thomée, Discrete time Galerkin methods for a parabolic boundary value problem, Ann. Mat. Pura Appl., 101 (1974), 115-152.
doi: 10.1007/BF02417101. |
[2] |
R. F. Curtain, Disturbance decoupling by measurement feedback with stability for infinite dimensional systems, Internat. J. Control, 43 (1986), 1723-1743.
doi: 10.1080/00207178608933569. |
[3] |
R. F. Curtain, Invariance concepts in infinite dimensions, SIAM J. Control Optim., 24 (1986), 1009-1031.
doi: 10.1137/0324059. |
[4] |
R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems Theory, Lecture Notes in Control and Information Sciences, 8, Springer-Verlag, Berlin, 1978. |
[5] |
R. E. Edwards, Fourier Series, a Modern Introduction, vol.II, $2^{nd}$ edition, Springer-Verlag, New York, 1982. |
[6] |
L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, vol. 19, American Mathematical Society, 1998. |
[7] |
K. A. Morris and R. Rebarber, Feedback invariance of SISO infinite dimensional systems, Math. Control Signals Systems, 19 (2007), 311-335.
doi: 10.1007/s00498-007-0021-9. |
[8] |
L. Pandolfi, Disturbance decoupling and invariant subspaces for delay systems, Appl. Math. Optim., 14 (1986), 55-72.
doi: 10.1007/BF01442228. |
[9] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[10] |
E. J. P. G. Schmidt and R. J. Stern, Invariance theory for infinite dimensional linear control systems, Appl. Math. Optim., 6 (1980), 113-122.
doi: 10.1007/BF01442887. |
[11] |
J. M. Schumacher, A direct approach to compensator design for distributed parameter systems, SIAM J. Control Optim., 21 (1983), 823-836.
doi: 10.1137/0321050. |
[12] |
H. L. Trentelman, Almost Invariant Subspaces and High Gain Feedback, Ph.D thesis, Rijksuniversiteit Groningen, 1986. |
[13] |
J. C. Willems, Almost invariant subspaces: An approach to high gain feedback design-part I: Almost controlled invariant subspaces, IEEE Trans. Automat. Control, 26 (1981), 235-252.
doi: 10.1109/TAC.1981.1102551. |
[14] |
J. L. Willems, Disturbance isolation in linear feedback systems, Int. J. Syst. Sci., 6 (1975), 233-238.
doi: 10.1080/00207727508941812. |
[15] |
W. M. Wonham, Linear Multivariable Control: A Geometric Approach, $2^{nd}$ edition, Springer-Verlag, New York, 1979. |
[16] |
H. J. Zwart, Geometric Theory for Infinite Dimensional Systems, Lecture Notes in Control and Information Sciences, 115, Springer-Verlag, Berlin, 1989.
doi: 10.1007/BFb0044353. |
[17] |
H. J. Zwart, Equivalence between open-loop and closed-loop invariance for infinite-dimensional systems: a frequency domain approach, SIAM J. Control Optim., 26 (1988), 1175-1199.
doi: 10.1137/0326065. |
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