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

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1. Ancona, F. and Coclite, G.M. (2005). On the boundary controllability of first-order hyperbolic systems, Nonlinear Analysis: Theory, Methods & Applications 63(5-7): e1955-e1966. Zbl1224.93010
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, Applied Thermal Engineering 27(13): 2332-2338. 
3. Bartecki, K. (2007). Comparison of frequency responses of parallel- and counter-flow type of heat exchanger, Proceedings of the 13th IEEE IFAC International Conference on Methods and Models in Automation and Robotics, Szczecin, Poland, pp. 411-416. 
4. Bartecki, K. (2009). Frequency- and time-domain analysis of a simple pipeline system, Proceedings of the 14th IEEE IFAC International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 366-371. 
5. Bartecki, K. (2010). On some peculiarities of neural network approximation applied to the inverse kinematics problem, Proceedings of the Conference on Control and FaultTolerant Systems, Nice, France, pp. 317-322. 
6. Bartecki, K. (2011). Approximation of a class of distributed parameter systems using proper orthogonal decomposition, Proceedings of the 16th IEEE International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 351-356. 
7. Bartecki, K. (2012a). Neural network-based PCA: An application to approximation of a distributed parameter system, in L., Rutkowski, M., Korytkowski, R., Scherer, R., Tadeusiewicz, L. Zadeh and J. Zurada (Eds.), Artificial Intelligence and Soft Computing, Lecture Notes in Computer Science, Vol. 7267, Springer, Berlin/Heidelberg, pp. 3-11. 
8. Bartecki, K. (2012b). PCA-based approximation of a class of distributed parameter systems: Classical vs. neural network approach, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(3): 651-660. 
9. Bartecki, K. and Rojek, R. (2005). Instantaneous linearization of neural network model in adaptive control of heat exchange process, Proceedings of the 11th IEEE International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 967-972. 
10. Bounit, H. (2003). The stability of an irrigation canal system, International Journal of Applied Mathematics and Computer Science 13(4): 453-468. Zbl1115.93333
11. Callier, F.M. and Winkin, J. (1993). Infinite dimensional system transfer functions, in R.F, Curtain, A. Bensoussan and J.L. Lions (Eds.), Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems, Lecture Notes in Control and Information Sciences, Vol. 185, Springer, Berlin/Heidelberg, pp. 75-101. Zbl0793.93040
12. Cheng, A. and Morris, K. (2003). Well-posedness of boundary control systems, SIAM Journal on Control and Optimization 42(4): 1244-1265. Zbl1049.35041
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 $L^{\infty }$-coefficients, Journal of Differential Equations 246(3): 1119-1138. Zbl1160.35045
14. Christofides, P.D. and Daoutidis, P. (1997). Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds, Journal of Mathematical Analysis and Applications 216(2): 398-420. Zbl0890.93051
15. Christofides, P.D. and Daoutidis, P. (1998a). Distributed output feedback control of two-time-scale hyperbolic PDE systems, Applied Mathematics and Computer Science 8(4): 713-732. Zbl0981.93045
16. Christofides, P.D. and Daoutidis, P. (1998b). Robust control of hyperbolic PDE systems, Chemical Engineering Science 53(1): 85-105. Zbl0981.93045
17. Contou-Carrere, M.N. and Daoutidis, P. (2008). Model reduction and control of multi-scale reaction-convection processes, Chemical Engineering Science 63(15): 4012-4025. 
18. Coron, J., d'Andrea Novel, B. and Bastin, G. (2007). A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws, IEEE Transactions on Automatic Control 52(1): 2-11. 
19. Curtain, R.F. (1988). Equivalence of input-output stability and exponential stability for infinite-dimensional systems, Mathematical Systems Theory 21(1): 19-48. Zbl0657.93050
20. Curtain, R.F., Logemann, H., Townley, S. and Zwart, H. (1992). Well-posedness, stabilizability, and admissibility for Pritchard-Salamon systems, Journal of Mathematical Systems, Estimation, and Control 4(4): 1-38. Zbl0815.93046
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, International Journal of Control 74(12): 1260-1270. Zbl1011.93024
22. Curtain, R.F. and Weiss, G. (2006). Exponential stabilization of well-posed systems by colocated feedback, SIAM Journal on Control and Optimization 45(1): 273-297. Zbl1139.93026
23. Curtain, R.F. and Zwart, H. (1995). An Introduction to InfiniteDimensional Linear Systems Theory, Springer-Verlag, New York, NY. Zbl0839.93001
24. Curtain, R. and Morris, K. (2009). Transfer functions of distributed parameters systems: A tutorial, Automatica 45(5): 1101-1116. Zbl1162.93300
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, HVAC&R Research 10(1): 21-31. 
26. Diagne, A., Bastin, G. and Coron, J.-M. (2012). Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws, Automatica 48(1): 109-114. Zbl1244.93143
27. Ding, L., Johansson, A. and Gustafsson, T. (2009). Application of reduced models for robust control and state estimation of a distributed parameter system, Journal of Process Control 19(3): 539-549. 
28. Dooge, J.C.I. and Napiorkowski, J.J. (1987). The effect of the downstream boundary conditions in the linearized St Venant equations, The Quarterly Journal of Mechanics and Applied Mathematics 40(2): 245-256. Zbl0611.76049
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, Automatica 44(5): 1310-1318. Zbl1283.93211
30. Evans, L.C. (1998). Partial Differential Equations, American Mathematical Society, Providence, RI. Zbl0902.35002
31. Filbet, F. and Shu, C.-W. (2005). Approximation of hyperbolic models for chemosensitive movement, SIAM Journal on Scientific Computing 27(3): 850-872. Zbl1141.35396
32. Friedly, J.C. (1972). Dynamic Behaviour of Processes, Prentice Hall, New York, NY. 
33. Górecki, H., Fuksa, S., Grabowski, P. and Korytowski, A. (1989). Analysis and Synthesis of Time Delay Systems, Wiley, New York, NY. Zbl0695.93002
34. Grabowski, P. and Callier, F.M. (2001a). Boundary control systems in factor form: Transfer functions and input-output maps, Integral Equations and Operator Theory 41(1): 1-37. Zbl1009.93041
35. Grabowski, P. and Callier, F.M. (2001b). Circle criterion and boundary control systems in factor form: Input-output approach, International Journal of Applied Mathematics and Computer Science 11(6): 1387-1403. Zbl0999.93061
36. Gvozdenac, D.D. (1990). Transient response of the parallel flow heat exchanger with finite wall capacitance, Archive of Applied Mechanics 60(7): 481-490. 
37. Jacob, B. and Zwart, H.J. (2012). Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces, Operator Theory: Advances and Applications, Vol. 223, Springer-Verlag, Basel. Zbl1254.93002
38. Jones, B.L. and Kerrigan, E.C. (2010). When is the discretization of a spatially distributed system good enough for control?, Automatica 46(9): 1462-1468. Zbl1201.93027
39. Jovanović, M.R. and Bamieh, B. (2006). Computation of the frequency responses for distributed systems with one spatial variable, Systems Control Letters 55(1): 27-37. Zbl1129.93421
40. Kowalewski, A. (2009). Time-optimal control of infinite order hyperbolic systems with time delays, International Journal of Applied Mathematics and Computer Science 19(4): 597-608, DOI: 10.2478/v10006-009-0047-x. Zbl1300.49007
41. Li, H.-X. and Qi, C. (2010). Modeling of distributed parameter systems for applications: A synthesized review from time-space separation, Journal of Process Control 20(8): 891-901. 
42. Litrico, X. and Fromion, V. (2009a). Boundary control of hyperbolic conservation laws using a frequency domain approach, Automatica 45(3): 647-656. Zbl1168.93015
43. Litrico, X. and Fromion, V. (2009b). Modeling and Control of Hydrosystems, Springer, London. Zbl1168.93015
44. Litrico, X., Fromion, V. and Scorletti, G. (2007). Robust feedforward boundary control of hyperbolic conservation laws, Networks and Heterogeneous Media 2(4): 717-731. Zbl1165.35321
45. Lumer, G. and Phillips, R.S. (1961). Dissipative operators in a Banach space, Pacific Journal of Mathematics 11(2): 679-698. Zbl0101.09503
46. Maidi, A., Diaf, M. and Corriou, J.-P. (2010). Boundary control of a parallel-flow heat exchanger by input-output linearization, Journal of Process Control 20(10): 1161-1174. 
47. Mattheij, R.M.M., Rienstra, S.W. and ten Thije Boonkkamp, J.H.M. (2005). Partial Differential Equations: Modeling, Analysis, Computation, Society for Industrial and Applied Mathematics, Philadelphia, PA. Zbl1090.35001
48. Miano, G. and Maffucci, A. (2001). Transmission Lines and Lumped Circuits, Academic Press, San Diego, CA. Zbl1157.78317
49. Park, H.M. and Cho, D.H. (1996). The use of the Karhunen-Loève decomposition for the modeling of distributed parameter systems, Chemical Engineering Science 51(1): 81-98. 
50. Patan, M. (2012). Distributed scheduling of sensor networks for identification of spatio-temporal processes, International Journal of Applied Mathematics and Computer Science 22(2): 299-311, DOI: 10.2478/v10006-012-0022-9. Zbl1283.93298
51. Phillips, R.S. (1957). Dissipative hyperbolic systems, Transactions of the American Mathematical Society 86(1): 109-173. Zbl0081.31102
52. Pritchard, A.J. and Salamon, D. (1984). The linear quadratic optimal control problem for infinite dimensional systems with unbounded input and output operators, in F. Kappel and W. Schappacher (Eds.), Infinite-Dimensional Systems, Lecture Notes in Mathematics, Vol. 1076, Springer, Berlin/Heidelberg, pp. 187-202. Zbl0545.93042
53. Rabenstein, R. (1999). Transfer function models for multidimensional systems with bounded spatial domains, Mathematical and Computer Modelling of Dynamical Systems 5(3): 259-278. Zbl0935.93038
54. Rauch, J. and Taylor, M. (1974). Exponential decay of solutions to hyperbolic equations in bounded domains, Indiana University Mathematical Journal 24(1): 79-86. Zbl0281.35012
55. Salamon, D. (1987). Infinite dimensional linear systems with unbounded control and observation: A functional analytic approach, Transactions of the American Mathematical Society 300(2): 383-431. Zbl0623.93040
56. Sasane, A. (2002). Hankel Norm Approximation for Infinitedimensional Systems, Springer-Verlag, Berlin. Zbl1009.93501
57. Staffans, O.J. and Weiss, G. (2000). Transfer functions of regular linear systems, Part II: The system operator and the Lax-Phillips semigroup, Transactions of the American Mathematical Society 354(8): 3229-3262. Zbl0996.93012
58. Strikwerda, J. (2004). Finite Difference Schemes and Partial Differential Equations, Society for Industrial and Applied Mathematics, Philadelphia, PA. Zbl1071.65118
59. Sutherland, J.C. and Kennedy, C.A. (2003). Improved boundary conditions for viscous, reacting, compressible flows, Journal of Computational Physics 191(2): 502-524. Zbl1134.76736
60. Tucsnak, M. and Weiss, G. (2006). Passive and Conservative Linear Systems, Nancy University, Nancy. 
61. Tucsnak, M. and Weiss, G. (2009). Observation and Control for Operator Semigroups, Birkhäuser, Basel. Zbl1188.93002
62. Uciński, D. (2012). Sensor network scheduling for identification of spatially distributed processes, International Journal of Applied Mathematics and Computer Science 22(1): 25-40, DOI: 10.2478/v10006-012-0002-0. Zbl1273.93168
63. Weiss, G. (1994). Transfer functions of regular linear systems, Part I: Characterizations of regularity, Transactions of the American Mathematical Society 342(2): 827-854. Zbl0798.93036
64. Wu, W. and Liou, C.-T. (2001). Output regulation of two-time-scale hyperbolic PDE systems, Journal of Process Control 11(6): 637-647. 
65. Xu, C.-Z. and Sallet, G. (2002). Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems, ESAIM: Control, Optimisation and Calculus of Variations 7: 421-442. Zbl1040.93031
66. Zavala-Río, A., Astorga-Zaragoza, C.M. and Hernández-González, O. (2009). Bounded positive control for double-pipe heat exchangers, Control Engineering Practice 17(1): 136-145. 
67. Zwart, H. (2004). Transfer functions for infinite-dimensional systems, Systems and Control Letters 52(3-4): 247-255. Zbl1157.93420
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, ESAIM: Control, Optimisation and Calculus of Variations 16(04): 1077-1093. Zbl1202.93064

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