Skip to main content
Have a personal or library account? Click to login
A general transfer function representation for a class of hyperbolic distributed parameter systems Cover

A general transfer function representation for a class of hyperbolic distributed parameter systems

International Journal of Applied Mathematics and Computer Science
Volume 23 (2013): Issue 2 (June 2013)
By:   
Open Access
|Jun 2013
References

References

  1. Ancona, F. and Coclite, G.M. (2005). On the boundary controllability of first-order hyperbolic systems,(5-7): e1955-e1966.
    Open DOISearch in Google Scholar
  2. Arbaoui, M.A., Vernieres-Hassimi, L., Seguin, D. and Abdelghani-Idrissi, M.A. (2007). Counter-current tubular heat exchanger: Modeling and adaptive predictive functional control,(13): 2332-2338.
    Open DOISearch in Google Scholar
  3. Bartecki, K. (2007). Comparison of frequency responses of parallel- and counter-flow type of heat exchanger,, pp. 411-416.
    Search in Google Scholar
  4. Bartecki, K. (2009). Frequency- and time-domain analysis of a simple pipeline system,, pp. 366-371.
    Search in Google Scholar
  5. Bartecki, K. (2010). On some peculiarities of neural network approximation applied to the inverse kinematics problem,, pp. 317-322.
    Search in Google Scholar
  6. Bartecki, K. (2011). Approximation of a class of distributed parameter systems using proper orthogonal decomposition,, pp. 351-356.
    Search in Google Scholar
  7. Bartecki, K. (2012a). Neural network-based PCA: An application to approximation of a distributed parameter system,L., Rutkowski, M., Korytkowski, R., Scherer, R., Tadeusiewicz, L. Zadeh and J. Zurada (Eds.),, Lecture Notes in Computer Science, Vol. 7267, Springer, Berlin/Heidelberg, pp. 3-11.
    Search in Google Scholar
  8. Bartecki, K. (2012b). PCA-based approximation of a class of distributed parameter systems: Classical vs. neural network approach,(3): 651-660.
    Open DOISearch in Google Scholar
  9. Bartecki, K. and Rojek, R. (2005). Instantaneous linearization of neural network model in adaptive control of heat exchange process,, pp. 967-972.
    Search in Google Scholar
  10. Bounit, H. (2003). The stability of an irrigation canal system,(4): 453-468.
    Search in Google Scholar
  11. Callier, F.M. and Winkin, J. (1993). Infinite dimensional system transfer functions,R.F, Curtain, A. Bensoussan and J.L. Lions (Eds.),, Lecture Notes in Control and Information Sciences, Vol. 185, Springer, Berlin/Heidelberg, pp. 75-101.
    Open DOISearch in Google Scholar
  12. Cheng, A. and Morris, K. (2003). Well-posedness of boundary control systems,(4): 1244-1265.
    Open DOISearch in Google Scholar
  13. Chentouf, B. and Wang, J.M. (2009). Boundary feedback stabilization and Riesz basis property of a 1-D first order hyperbolic linear system with-coefficients,(3): 1119-1138.
    Open DOISearch in Google Scholar
  14. Christofides, P.D. and Daoutidis, P. (1997). Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds,(2): 398-420.
    Open DOISearch in Google Scholar
  15. Christofides, P.D. and Daoutidis, P. (1998a). Distributed output feedback control of two-time-scale hyperbolic PDE systems,(4): 713-732.
    Search in Google Scholar
  16. Christofides, P.D. and Daoutidis, P. (1998b). Robust control of hyperbolic PDE systems,(1): 85-105.
    Open DOISearch in Google Scholar
  17. Contou-Carrere, M.N. and Daoutidis, P. (2008). Model reduction and control of multi-scale reaction-convection processes,(15): 4012-4025.
    Open DOISearch in Google Scholar
  18. Coron, J., d’Andrea Novel, B. and Bastin, G. (2007). A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws,(1): 2-11.
    Open DOISearch in Google Scholar
  19. Curtain, R.F. (1988). Equivalence of input-output stability and exponential stability for infinite-dimensional systems,(1): 19-48.
    Open DOISearch in Google Scholar
  20. Curtain, R.F., Logemann, H., Townley, S. and Zwart, H. (1992). Well-posedness, stabilizability, and admissibility for Pritchard-Salamon systems,(4): 1-38.
    Search in Google Scholar
  21. Curtain, R.F. and Sasane, A.J. (2001). Compactness and nuclearity of the Hankel operator and internal stability of infinite-dimensional state linear systems,(12): 1260-1270.
    Open DOISearch in Google Scholar
  22. Curtain, R.F. and Weiss, G. (2006). Exponential stabilization of well-posed systems by colocated feedback,(1): 273-297.
    Open DOISearch in Google Scholar
  23. Curtain, R.F. and Zwart, H. (1995)., Springer-Verlag, New York, NY.
    Open DOISearch in Google Scholar
  24. Curtain, R. and Morris, K. (2009). Transfer functions of distributed parameters systems: A tutorial,(5): 1101-1116.
    Open DOISearch in Google Scholar
  25. Delnero, C.C., Dreisigmeyer, D., Hittle, D.C., Young, P.M., Anderson, C.W. and Anderson, M.L. (2004). Exact solution to the governing PDE of a hot water-to-air finned tube cross-flow heat exchanger,(1): 21-31.
    Open DOISearch in Google Scholar
  26. Diagne, A., Bastin, G. and Coron, J.-M. (2012). Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws,(1): 109-114.
    Open DOISearch in Google Scholar
  27. Ding, L., Johansson, A. and Gustafsson, T. (2009). Application of reduced models for robust control and state estimation of a distributed parameter system,(3): 539-549.
    Open DOISearch in Google Scholar
  28. Dooge, J.C.I. and Napiorkowski, J.J. (1987). The effect of the downstream boundary conditions in the linearized St Venant equations,(2): 245-256.
    Open DOISearch in Google Scholar
  29. Dos Santos, V., Bastin, G., Coron, J.-M. and d’Andréa Novel, B. (2008). Boundary control with integral action for hyperbolic systems of conservation laws: Stability and experiments,(5): 1310-1318.
    Open DOISearch in Google Scholar
  30. Evans, L.C. (1998)., American Mathematical Society, Providence, RI.
    Search in Google Scholar
  31. Filbet, F. and Shu, C.-W. (2005). Approximation of hyperbolic models for chemosensitive movement,(3): 850-872.
    Open DOISearch in Google Scholar
  32. Friedly, J.C. (1972)., Prentice Hall, New York, NY.
    Search in Google Scholar
  33. Górecki, H., Fuksa, S., Grabowski, P. and Korytowski, A. (1989)., Wiley, New York, NY.
    Search in Google Scholar
  34. Grabowski, P. and Callier, F.M. (2001a). Boundary control systems in factor form: Transfer functions and input-output maps,(1): 1-37.
    Open DOISearch in Google Scholar
  35. Grabowski, P. and Callier, F.M. (2001b). Circle criterion and boundary control systems in factor form: Input-output approach,(6): 1387-1403.
    Search in Google Scholar
  36. Gvozdenac, D.D. (1990). Transient response of the parallel flow heat exchanger with finite wall capacitance,(7): 481-490.
    Open DOISearch in Google Scholar
  37. Jacob, B. and Zwart, H.J. (2012)., Operator Theory: Advances and Applications, Vol. 223, Springer-Verlag, Basel.
    Search in Google Scholar
  38. Jones, B.L. and Kerrigan, E.C. (2010). When is the discretization of a spatially distributed system good enough for control?,(9): 1462-1468.
    Open DOISearch in Google Scholar
  39. Jovanovi´c, M.R. and Bamieh, B. (2006). Computation of the frequency responses for distributed systems with one spatial variable,(1): 27-37.
    Open DOISearch in Google Scholar
  40. Kowalewski, A. (2009). Time-optimal control of infinite order hyperbolic systems with time delays,(4): 597-608, DOI: 10.2478/v10006-009-0047-x.
    Open DOISearch in Google Scholar
  41. Li, H.-X. and Qi, C. (2010). Modeling of distributed parameter systems for applications: A synthesized review from time-space separation,(8): 891-901.
    Open DOISearch in Google Scholar
  42. Litrico, X. and Fromion, V. (2009a). Boundary control of hyperbolic conservation laws using a frequency domain approach,(3): 647-656.
    Open DOISearch in Google Scholar
  43. Litrico, X. and Fromion, V. (2009b)., Springer, London.
    Open DOISearch in Google Scholar
  44. Litrico, X., Fromion, V. and Scorletti, G. (2007). Robust feedforward boundary control of hyperbolic conservation laws,(4): 717-731.
    Open DOISearch in Google Scholar
  45. Lumer, G. and Phillips, R.S. (1961). Dissipative operators in a Banach space,(2): 679-698.
    Open DOISearch in Google Scholar
  46. Maidi, A., Diaf, M. and Corriou, J.-P. (2010). Boundary control of a parallel-flow heat exchanger by input-output linearization,(10): 1161-1174.
    Open DOISearch in Google Scholar
  47. Mattheij, R.M.M., Rienstra, S.W. and ten Thije Boonkkamp, J.H.M. (2005)., Society for Industrial and Applied Mathematics, Philadelphia, PA.
    Open DOISearch in Google Scholar
  48. Miano, G. and Maffucci, A. (2001)., Academic Press, San Diego, CA.
    Search in Google Scholar
  49. Park, H.M. and Cho, D.H. (1996). The use of the Karhunen-Loève decomposition for the modeling of distributed parameter systems,(1): 81-98.
    Open DOISearch in Google Scholar
  50. Patan, M. (2012). Distributed scheduling of sensor networks for identification of spatio-temporal processes,(2): 299-311, DOI: 10.2478/v10006-012-0022-9.
    Open DOISearch in Google Scholar
  51. Phillips, R.S. (1957). Dissipative hyperbolic systems,(1): 109-173.
    Open DOISearch in Google Scholar
  52. Pritchard, A.J. and Salamon, D. (1984). The linear quadratic optimal control problem for infinite dimensional systems with unbounded input and output operators,F. Kappel and W. Schappacher (Eds.),, Lecture Notes in Mathematics, Vol. 1076, Springer, Berlin/Heidelberg, pp. 187-202.
    Open DOISearch in Google Scholar
  53. Rabenstein, R. (1999). Transfer function models for multidimensional systems with bounded spatial domains,(3): 259-278.
    Open DOISearch in Google Scholar
  54. Rauch, J. and Taylor, M. (1974). Exponential decay of solutions to hyperbolic equations in bounded domains,(1): 79-86.
    Open DOISearch in Google Scholar
  55. Salamon, D. (1987). Infinite dimensional linear systems with unbounded control and observation: A functional analytic approach,(2): 383-431.
    Open DOISearch in Google Scholar
  56. Sasane, A. (2002)., Springer-Verlag, Berlin.
    Search in Google Scholar
  57. Staffans, O.J. and Weiss, G. (2000). Transfer functions of regular linear systems, Part II: The system operator and the Lax-Phillips semigroup,(8): 3229-3262.
    Open DOISearch in Google Scholar
  58. Strikwerda, J. (2004)., Society for Industrial and Applied Mathematics, Philadelphia, PA.
    Open DOISearch in Google Scholar
  59. Sutherland, J.C. and Kennedy, C.A. (2003). Improved boundary conditions for viscous, reacting, compressible flows,(2): 502-524.
    Open DOISearch in Google Scholar
  60. Tucsnak, M. and Weiss, G. (2006)., Nancy University, Nancy.
    Search in Google Scholar
  61. Tucsnak, M. and Weiss, G. (2009)., Birkhäuser, Basel.
    Open DOISearch in Google Scholar
  62. Uci´nski, D. (2012). Sensor network scheduling for identification of spatially distributed processes,(1): 25-40, DOI: 10.2478/v10006-012-0002-0.
    Open DOISearch in Google Scholar
  63. Weiss, G. (1994). Transfer functions of regular linear systems, Part I: Characterizations of regularity,(2): 827-854.
    Open DOISearch in Google Scholar
  64. Wu, W. and Liou, C.-T. (2001). Output regulation of two-time-scale hyperbolic PDE systems,(6): 637-647.
    Open DOISearch in Google Scholar
  65. Xu, C.-Z. and Sallet, G. (2002). Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems,: 421-442.
    Open DOISearch in Google Scholar
  66. Zavala-Río, A., Astorga-Zaragoza, C.M. and Hernández-González, O. (2009). Bounded positive control for double-pipe heat exchangers,(1): 136-145.
    Open DOISearch in Google Scholar
  67. Zwart, H. (2004). Transfer functions for infinite-dimensional systems,(3-4): 247-255.
    Open DOISearch in Google Scholar
  68. Zwart, H., Gorrec, Y.L., Maschke, B. and Villegas, J. (2010). Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain,(04): 1077-1093.
    Open DOISearch in Google Scholar
DOI: https://doi.org/10.2478/amcs-2013-0022 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Journal RSS Feed
Language: English
Page range: 291 - 307
Published on: Jun 28, 2013
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
distributed parameter system,
hyperbolic system,
partial differential equation,
transfer function,
heat exchanger
Related subjects:
Mathematics,
Applied mathematics

© 2013 Krzysztof Bartecki, published by University of Zielona Góra
This work is licensed under the Creative Commons License.

Volume 23 (2013): Issue 2 (June 2013)
Previous article
Next article