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Sistemas Lineales Variantes en el tiempo (SLVT) y Sistemas Lineales
Lentamente variables en el tiempo (SLLVT)
1. Sistemas lineales variantes en el tiempo
Capítulos de libros que tratan sobre sistemas lineales variantes en el
tiempo y/o sistemas periódicos:
- F. Verhulst, Linear Equations,
Capítulo 6 de Nonlinear Differential Equations and Dynamical
Systems, 2da. Edición,. Springer-Verlag Berlin, 1996.
- W. J. Rugh, Additional Stability
Criteria, Capítulo 8 de Linear System Theory,
2da. Edición. Prentice Hall, Upper Saddle River, N. J. , 1996.
- E. W. Kamen, Fundamentals of Time-Varying
Linear Systems, Capítulo 25 en The Control Engineering
Handbook, R. Levine (ed.), CRC Press, Inc., 1996. pp. 451-468.
Artículos sobre sistemas lineales variantes en el tiempo
- I. Lewkowicz, A necessary condition
for quantitative exponential stability of linear state space systems, Proceedings
of the 37th IEEE Conference on Decision and Control, 16-18 Dec. 1998, Vol.
1, pp. 624 -625.
- I. Lewkowicz, A necessary condition
for quantitative exponential stability of linear state-space systems, Systems
& Control Letters, Vol. 38, 1999, pp. 1–4.
- J.-J. Fuchs, On the good use of the
spectral radius of a matrix, IEEE Transactions on Automatic Control,
Vol. 27, No. 5, Oct 1982, pp. 1134 -1135.
- D. Guo, W. J. Rugh, A Stability Result for Linear parameter-varying systems.
Systems & Control Letters,
Vol. 24, 1995, pp. 1-5.
- P. G. Voulgaris, M .A. Dahleh, On
l-inf to l-inf performance of slowly varying systems. Systems
& Control Letters, Vol. 24, 1995, pp. 243-249.
- J. Jim Zhu, A
necessary and Sufficient Stability Criterion for Linear Time-Varying Systems,
Proceedings of the Twenty-Eigth Southeastern Symposium on
System Theory (28SSST '96), 31 March-2 April 1996,
pp. 115-119
- Stefan Fröhler, Ulrich Oberst, Continuous
time-varying linear systems, Systems & Control Letters,
Vol. 35, 1998, pp. 97–110.
- G. E. Dullerud, S. Lall, A New Approach
for Analysis and Synthesis of Time-Varying Systems, IEEE Transactions
on Automatic Control, Vol. 44, No. 8, August 1999, pp. 1486-1497.
- N. M. Linh, V. N. Phat, Exponential
stability of nonlinear time-varying differential equations and applications,
Electronic Journal of Differential Equations, Vol. 2001,
2001, No. 34, pp. 1-13.
- M. de la Sen, Robust stability of
a class of linear time-varying systems, IMA Journal of
Mathematical Control and Information, Vol. 19, 2002, pp. 399–418.
- D. Liu, A. Molchanov, Criteria for
robust absolute stability of time-varying nonlinear continuous-time systems,
Automatica, Vol. 38, 2002, pp. 627 – 637.
- A. Loría, E. Panteley, Uniform
exponential stability of linear time-varying systems: revisited, Systems
& Control Letters, Vol. 47, 2002, pp. 13 – 24.
- R. E. Bartels, A Numerical
Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear
Coefficients Based on the State Transition Matrix, Nasa
Report NASA/TM-2002-211776, August 2002.
- G. S. Christensen,
Uniform Asymptotic Stability of Linear Non-Autonomous Systems,
Can J. Elect. Comp. Eng., Vol 28, No. 2/4, July/October
2003, pp. 173-176
- Comentario sobre las cotas de Vidyasagar:
En la p. 249, se dice que la cota m
(ec. 5.8.2.17, p. 248) es el máximo del número de condición de A(t)
cuando t varía. Sin embargo, esto no es necesariamente cierto, ya que
este es un problema no resuelto de la Teoría de Control. Vea:
D. Hinrichsen, E. Plischke, F. Wirth,
Robustness of
transient behavior , Problema 6.3 de Unsolved Problems in Mathematical
Systems and Control Theory, D. Blondel, A. Megretsky (eds.), Princeton
University Press, Princeton, EE.UU., 2004, pp. 197-202.
(Disponible electrónicamente en
http://pup.princeton.edu/math/ y
en
http://www.inma.ucl.ac.be/~blondel/op/ )
(3/12/04)
2. Sistemas lineales lentamente variantes en el tiempo
- L. Markus, H. Yamabe, Global
Stability Criteria for Differential Systems, Osaka Math
Jorunal, Vol. 12, 1960, pp. 305-317.
- C. Desoer, Slowly varying system x
= A(t)x, IEEE Transactions on Automatic Control,
Vol. 14, No. 6, Dec 1969, pp. 780 -781.
- R. Skoog, C. Lau, Instability
of slowly varying systems, IEEE Transactions on
Automatic Control, Vol. 17, No. 1, Feb. 1972, pp. 86 -92.
- G. Shanholt, Slowly varying linear
functional differential equations, IEEE Transactions on Automatic Control,
Vol. 17, No. 1, Feb 1972, pp. 166 -167.
- F. Amato, G. Celentano, F. Garofalo, New
sufficient conditions for the stability of slowly varying linear systems, IEEE
Transactions on Automatic Control, Vol. 38, No. 9, Sept. 1993, pp. 1409
-1411.
- P. A. Cook, Stability of Linear Systems
with Slowly Changing Parameters, C. S. C. Report No.
881, Control Systems Centre. Department of Electrical Engineering and
Electronics, UMIST, Manchester, U.K., June 1999.
3. Sistemas periódicos
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