- C.D. Benchimol, A note on weak stabilizability of contraction semigroups. SIAM J. Control Optim. 16 (1978) 373-379. [CrossRef]
- H. Bounit, H. Hammouri and J. Sau, Regulation of an irrigation canal system through the semigroup approach, in Proc. of the International Workshop Regulation of Irrigation Canals: State of the Art of Research and Applications. Marocco (1997) 261-267.
- S.X. Chen, Introduction to partial differential equations. People Education Press (in Chinese) (1981).
- V.T. Chow, Open channel hydraulics. Mac-GrawHill Book Company, New York (1985).
- J.M. Coron, B. d'Andréa-Novel and G. Bastin, A Lyapunov approach to control irrigation canals modeled by Saint-Venant equations, in European Control Conference ECC'99. Karlsruhe (1999).
- R.F. Curtain, Equivalence of input-output stability and exponential stability for infinite-dimensional systems. Math. Systems Theory 21 (1988) 19-48. [CrossRef] [MathSciNet]
- C. Foias, H. Özbay and A. Tannenbaum, Robust Control of Infinite Dimensional Systems. Frequency Domain Methods. Springer, Hong Kong, Lecture Notes in Control and Inform. Sci. 209 (1996).
- B.A. Francis and G. Zames, On -optimal sensitivity theory for SISO feedback systems. IEEE Trans. Automat. Control 29 (1984) 9-16. [CrossRef] [MathSciNet]
- J.C. Friedly, Dynamic Behavior of Processes. Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1972).
- J.P. Gauthier and C.Z. Xu, -control of a distributed parameter system with non-minimum phase. Int. J. Control 53 (1991) 45-79. [CrossRef]
- K.M. Hangos, A.A. Alonso, J.D. Perkins and B.E. Ydstie, Thermodynamic approach to the structural stability of process plants. AIChE J. 45 (1999) 802-816. [CrossRef]
- H. Hoffman, Banach Spaces of Analytic Functions. Prentice-Hall Inc., Englewood Cliffs (1962).
- F.L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces. Ann. Differential Equations 1 (1985) 43-56. [MathSciNet]
- H.O. Kreiss, O.E. Ortiz and O.A. Reula, Stability of quasi-linear hyperbolic dissipative systems. J. Differential Equations 142 (1998) 78-96. [CrossRef] [MathSciNet]
- P.D. Lax and R.S. Phillips, Local boundary conditions for dissipative symmetric linear differential operators. Comm. Pure Appl. Math. 13 (1960) 427-455. [CrossRef] [MathSciNet]
- T.S. Li, Global Classical Solutions for Quasilinear Hyperbolic Systems, Research in Applied Mathematics, edited by P.G. Ciarlet and J.-L. Lions. John Willey & Sons, New York (1994).
- H. Logemann, E.P. Ryan and S. Townley, Integral control of infinite-dimensional linear systems subject to input saturation. SIAM J. Control Optim. 36 (1998) 1940-1961. [CrossRef] [MathSciNet]
- H. Logemann and S. Townley, Low gain control of uncertain regular linear systems. SIAM J. Control Optim. 35 (1997) 78-116. [CrossRef] [MathSciNet]
- K.A. Morris, Justification of input/output methods for systems with unbounded control and observation. IEEE Trans. Automat. Control 44 (1999) 81-85. [CrossRef] [MathSciNet]
- O.E. Ortiz, Stability of nonconservative hyperbolic systems and relativistic dissipative fluids. J. Math. Phys. 42 (2001) 1426-1442. [CrossRef] [MathSciNet]
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York (1983).
- S.A. Pohjolainen, Robust multivariable PI-controllers for infinite dimensional systems. IEEE Trans. Automat. Control 27 (1985) 17-30. [CrossRef]
- J. Prüss, On the spectrum of C0-semigroups. Trans. Amer. Math. Soc. 284 (1984) 847-857. [CrossRef] [MathSciNet]
- J. Rauch, Symmetric positive systems with boundary characteristic of constant multiplicity. Trans. Amer. Math. Soc. 291 (1985) 167-187. [CrossRef] [MathSciNet]
- J. Rauch and M. Taylor, Exponential decay of solutions to hyperbolic equations in bounded domain. Indiana Univ. Math. J. 24 (1974) 79-86. [CrossRef] [MathSciNet]
- R. Rebarber, Conditions for the equivalence of internal and external stability for distributed parameter systems. IEEE Trans. Automat. Control 38 (1993) 994-998. [CrossRef] [MathSciNet]
- D.L. Russell, Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions. SIAM Rev. 20 (1978) 639-739. [CrossRef] [MathSciNet]
- D. Salamon, Realization theory in Hilbert space. Math. Systems Theory 21 (1989) 147-164. [CrossRef] [MathSciNet]
- O.J. Staffans, Feedback representations of critical controls for well-posed linear systems. Int. J. Robust Nonlinear Control 8 (1998) 1189-1217. [CrossRef]
- G. Weiss, Admissible observation operators for linear semigroups. Israel J. Math. 65 (1989) 17-43. [CrossRef] [MathSciNet]
- G. Weiss, Regular linear systems with feedback. Math. Control, Signals & Systems 7 (1994) 23-57.
- G. Weiss, Transfer functions of regular linear systems. Part I: Characterizations of regularity. Trans. Amer. Math. Soc. 342 (1994) 827-854. [CrossRef] [MathSciNet]
- G. Weiss and R.F. Curtain, Dynamic stabilization of regular linear systems. IEEE Trans. Automat. Control 42 (1997) 4-21. [CrossRef] [MathSciNet]
- C.Z. Xu and D.X. Feng, Linearization method to stability analysis for nonlinear hyperbolic systems. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 809-814.
- C.Z. Xu and J.P. Gauthier, Analyse et commande d'un échangeur thermique à contre-courant. RAIRO APII 25 (1991) 377-396.
- C.Z. Xu, J.P. Gauthier and I. Kupka, Exponential stability of the heat exchanger equation, in Proc. of the European Control Conference. Groningen, The Netherlands (1993) 303-307.
- C.Z. Xu and H. Jerbi, A robust PI-controller for infinite dimensional systems. Int. J. Control 61 (1995) 33-45. [CrossRef]
- C.Z. Xu, Exponential stability of a class of infinite dimensional time-varying linear systems, in Proc. of the International Conference on Control and Information. Hong Kong (1995).
- C.Z. Xu, Exact observability and exponential stability of infinite dimensional bilinear systems. Math. Control, Signals & Systems 9 (1996) 73-93.
- C.Z. Xu and G. Sallet, Proportional and Integral regulation of irrigation canal systems governed by the Saint-Venant equation, in 14th IFAC World Congress. Beijing, China (1999).
- C.Z. Xu and D.X. Feng, Symmetric hyperbolic systems and applications to exponential stability of heat exchangers and irrigation canals, in Proc. of the MTNS'2000. Perpignan (2000).
- B.E. Ydstie and A.A. Alonso, Process systems and passivity via the Clausius-Planck inequality. Systems Control Lett. 30 (1997) 253-264. [CrossRef] [MathSciNet]
Volume 7, 2002
|Page(s)||421 - 442|
|Published online||15 September 2002|