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Partial stabilizability and hidden convexity of indefinite LQ problem
Minimum sensitivity realizations of networks of linear systems
1. | Institute for Mathematics, University of Würzburg, Emil-Fischer Straße 40, 97074 Würzburg, Germany |
2. | Institute for Mathematics, University of Würzburg, Emil-Fischer Straße 40, 97074 Würzburg, Germany |
References:
[1] |
J. B. Cruz and W. R. Perkins, A new approach to the sensitivity problem in multivariable feedback system design, IEEE T. Automat. Contr., 9 (1964), 216-223. |
[2] |
D. F. Delchamps, New geometric approaches to parameter sensitivity in feedback systems, in Modelling, Identification and Robust Control(eds. C. I. Byrnes and A. Lindquist), Elsevier Science Publishers B. V. (North-Holland), (1986), 445-456. |
[3] |
R. Fornaro, Numerical evaluation of integrals around simple closed curves, SIAM J. Numer. Anal., 10 (1973), 623-634. |
[4] |
P. A. Fuhrmann and U. Helmke, Reachability, observability and strict equivalence of networks of linear systems, Math. Control Signal., 25 (2013), 437-471.
doi: 10.1007/s00498-012-0104-0. |
[5] |
P. A. Fuhrmann and U. Helmke, The Mathematics of Networks of Linear Systems, Cham: Springer, 2015.
doi: 10.1007/978-3-319-16646-9. |
[6] |
M. Gevers and G. Li, Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects, Springer, Berlin, 1993.
doi: 10.1007/978-1-4471-2039-1. |
[7] |
S. Hara, A unified approach to decentralized cooperative control for large-scale networked dynamical systems, in Perspectives in Mathematical System Theory, Control, and Signal Processing (eds. J. C. Willems et al.), Springer, Berlin, (2010), 61-72.
doi: 10.1007/978-3-540-93918-4_6. |
[8] |
S. Hara, T. Hayakawa and H. Sugata, LTI systems with generalized frequency variables: A unified framework for homogeneous multi-agent dynamical systems, SICE Journal of Control, Measurement, and Systems Integration, 2 (2009), 299-306. |
[9] |
U. Helmke, I. Kurniawan, P. Lang and M. Schönlein, Sensitivity optimal design of networks of identical linear systems, in Proc. Mathematical Theory of Networks and Systems (MTNS2012), Melbourne, Australia, 5-9 July 2012, paper 0283. |
[10] |
U. Helmke and J. B. Moore, L2 sensitivity minimization of linear system representations via gradient flows, J. Math. Syst. Estim. Control, 5 (1995), 79-98. |
[11] |
U. Helmke and J. B. Moore, Optimization and Dynamical Systems, Springer, London, 1994.
doi: 10.1007/978-1-4471-3467-1. |
[12] |
R. A. Horn and R. Mathias, Block-matrix generalizations of Schur's basic theorems on Hadamard products, Linear Algebra Appl., 172 (1992), 337-346.
doi: 10.1016/0024-3795(92)90033-7. |
[13] |
S. Koshita, M. Abe, and M. Kawamata, Analysis of second-order modes of linear discrete-time systems under bounded-real transformations, IEICE T. Fund. Electr., 90 (2007), 2510-2515. |
[14] |
S. Liu, Matrix results on the Khatri-Rao and Tracy-Singh products, Linear Algebra Appl., 289 (1998), 267-277.
doi: 10.1016/S0024-3795(98)10209-4. |
[15] |
J. Lunze, Control Theory of Digitally Networked Dynamic Systems, Cham: Springer, 2014.
doi: 10.1007/978-3-319-01131-8. |
[16] |
M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks, Princeton University Press, 2010.
doi: 10.1515/9781400835355. |
[17] |
B. Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE T. Automat. Contr., 26 (1981), 17-32.
doi: 10.1109/TAC.1981.1102568. |
[18] |
C. T. Mullis and R. A. Roberts, Roundoff noise in digital filters: frequency transformations and invariants, IEEE T. Acoust. Speech, 24 (1976), 538-550. |
[19] |
C. T. Mullis and R. A. Roberts, Synthesis of minimum roundoff noise fixed point digital filters, IEEE T. Circuits Syst., 23 (1976), 551-562. |
[20] |
R. Olfati-Saber, J. Fax, and R. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215-233. |
[21] |
L. Pernebo and L. M. Silverman, Model reduction via balanced state space representations, IEEE T. Automat. Contr., 27 (1982), 382-387.
doi: 10.1109/TAC.1982.1102945. |
[22] |
V. Tavsanoglu and L. Thiele, Optimal design of state-space digital filters by simultaneous minimization of sensitivity and roundoff noise, IEEE T. Automat. Contr., 31 (1984), 884-888.
doi: 10.1109/TCS.1984.1085426. |
[23] |
L. Thiele, On the sensitivity of linear state-space systems, IEEE T. Circuits Syst., 33 (1986), 502-510.
doi: 10.1109/TCS.1986.1085951. |
[24] |
W.-Y. Yan, J. B. Moore and U. Helmke, Recursive algorithms for solving a class of nonlinear matrix equations with applications to certain sensitivity optimization problems, SIAM J. Control Optim., 32 (1994), 1559-1576.
doi: 10.1137/S0363012992226855. |
[25] |
G. Zames, Functional analysis applied to nonlinear feedback systems, IEEE T. Circuits Syst., 10 (1963), 392-404. |
show all references
References:
[1] |
J. B. Cruz and W. R. Perkins, A new approach to the sensitivity problem in multivariable feedback system design, IEEE T. Automat. Contr., 9 (1964), 216-223. |
[2] |
D. F. Delchamps, New geometric approaches to parameter sensitivity in feedback systems, in Modelling, Identification and Robust Control(eds. C. I. Byrnes and A. Lindquist), Elsevier Science Publishers B. V. (North-Holland), (1986), 445-456. |
[3] |
R. Fornaro, Numerical evaluation of integrals around simple closed curves, SIAM J. Numer. Anal., 10 (1973), 623-634. |
[4] |
P. A. Fuhrmann and U. Helmke, Reachability, observability and strict equivalence of networks of linear systems, Math. Control Signal., 25 (2013), 437-471.
doi: 10.1007/s00498-012-0104-0. |
[5] |
P. A. Fuhrmann and U. Helmke, The Mathematics of Networks of Linear Systems, Cham: Springer, 2015.
doi: 10.1007/978-3-319-16646-9. |
[6] |
M. Gevers and G. Li, Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects, Springer, Berlin, 1993.
doi: 10.1007/978-1-4471-2039-1. |
[7] |
S. Hara, A unified approach to decentralized cooperative control for large-scale networked dynamical systems, in Perspectives in Mathematical System Theory, Control, and Signal Processing (eds. J. C. Willems et al.), Springer, Berlin, (2010), 61-72.
doi: 10.1007/978-3-540-93918-4_6. |
[8] |
S. Hara, T. Hayakawa and H. Sugata, LTI systems with generalized frequency variables: A unified framework for homogeneous multi-agent dynamical systems, SICE Journal of Control, Measurement, and Systems Integration, 2 (2009), 299-306. |
[9] |
U. Helmke, I. Kurniawan, P. Lang and M. Schönlein, Sensitivity optimal design of networks of identical linear systems, in Proc. Mathematical Theory of Networks and Systems (MTNS2012), Melbourne, Australia, 5-9 July 2012, paper 0283. |
[10] |
U. Helmke and J. B. Moore, L2 sensitivity minimization of linear system representations via gradient flows, J. Math. Syst. Estim. Control, 5 (1995), 79-98. |
[11] |
U. Helmke and J. B. Moore, Optimization and Dynamical Systems, Springer, London, 1994.
doi: 10.1007/978-1-4471-3467-1. |
[12] |
R. A. Horn and R. Mathias, Block-matrix generalizations of Schur's basic theorems on Hadamard products, Linear Algebra Appl., 172 (1992), 337-346.
doi: 10.1016/0024-3795(92)90033-7. |
[13] |
S. Koshita, M. Abe, and M. Kawamata, Analysis of second-order modes of linear discrete-time systems under bounded-real transformations, IEICE T. Fund. Electr., 90 (2007), 2510-2515. |
[14] |
S. Liu, Matrix results on the Khatri-Rao and Tracy-Singh products, Linear Algebra Appl., 289 (1998), 267-277.
doi: 10.1016/S0024-3795(98)10209-4. |
[15] |
J. Lunze, Control Theory of Digitally Networked Dynamic Systems, Cham: Springer, 2014.
doi: 10.1007/978-3-319-01131-8. |
[16] |
M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks, Princeton University Press, 2010.
doi: 10.1515/9781400835355. |
[17] |
B. Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE T. Automat. Contr., 26 (1981), 17-32.
doi: 10.1109/TAC.1981.1102568. |
[18] |
C. T. Mullis and R. A. Roberts, Roundoff noise in digital filters: frequency transformations and invariants, IEEE T. Acoust. Speech, 24 (1976), 538-550. |
[19] |
C. T. Mullis and R. A. Roberts, Synthesis of minimum roundoff noise fixed point digital filters, IEEE T. Circuits Syst., 23 (1976), 551-562. |
[20] |
R. Olfati-Saber, J. Fax, and R. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215-233. |
[21] |
L. Pernebo and L. M. Silverman, Model reduction via balanced state space representations, IEEE T. Automat. Contr., 27 (1982), 382-387.
doi: 10.1109/TAC.1982.1102945. |
[22] |
V. Tavsanoglu and L. Thiele, Optimal design of state-space digital filters by simultaneous minimization of sensitivity and roundoff noise, IEEE T. Automat. Contr., 31 (1984), 884-888.
doi: 10.1109/TCS.1984.1085426. |
[23] |
L. Thiele, On the sensitivity of linear state-space systems, IEEE T. Circuits Syst., 33 (1986), 502-510.
doi: 10.1109/TCS.1986.1085951. |
[24] |
W.-Y. Yan, J. B. Moore and U. Helmke, Recursive algorithms for solving a class of nonlinear matrix equations with applications to certain sensitivity optimization problems, SIAM J. Control Optim., 32 (1994), 1559-1576.
doi: 10.1137/S0363012992226855. |
[25] |
G. Zames, Functional analysis applied to nonlinear feedback systems, IEEE T. Circuits Syst., 10 (1963), 392-404. |
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