Free Access
Volume 20, Number 3, July-September 2014
Page(s) 894 - 923
Published online 13 June 2014
  1. O. Aamo, Disturbance Rejection in Linear Hyperbolic Systems. IEEE Trans. Autom. Control 58 (2013) 1095–1106. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Bastin and J.-M. Coron, Further Results on Boundary Feedback Stabilization of Hyperbolic Systems Over a Bounded Interval. In Proc. of IFAC Nolcos 2010, Bologna, Italy (2010). [Google Scholar]
  3. G. Bastin and J.-M. Coron, On Boundary Feedback Stabilization of Non-Uniform Linear Hyperbolic Systems Over a Bounded Interval. Syst. Control Lett. 60 (2011) 900–906. [Google Scholar]
  4. K.L. Cooke and D.W. Krumme, Differential-Difference Equations and Nonlinear Initial-Boundary Value Problems for Linear Hyperbolic Partial Differential Equations. J. Math. Anal. Appl. 24 (1968) 372–387. [Google Scholar]
  5. J.-M. Coron, G. Bastin and B. d’Andrea-Novel, Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems. SIAM J. Control Optim. 47 (2008) 1460–1498. [Google Scholar]
  6. J.-M. Coron, R. Vazquez, M. Krstic, and G. Bastin, Local Exponential H2 Stabilization of a Quasilinear Hyperbolic System Using Backstepping. SIAM J. Control Optim. 51 (2013) 2005–2035. [Google Scholar]
  7. A. Diagne, G. Bastin and J.-M. Coron, Lyapunov Exponential Stability of 1-d Linear Hyperbolic Systems of Balance Laws. Automatica 48 (2012) 109–114. [CrossRef] [MathSciNet] [Google Scholar]
  8. A.V. Fillipov, Differential Equations with Discontinuous Right-Hand Sides. Kluwer Academic Publishers, Dordrecht (1988). [Google Scholar]
  9. S.-Y. Ha and A. Tzavaras, Lyapunov Functionals and L1-Stability for Discrete Velocity Boltzmann Equations. Commun. Math. Phys. 239 (2003) 65–92. [CrossRef] [Google Scholar]
  10. J.K. Hale and S.M.V. Lunel, Introduction to Functional Differential Equations. Springer-Verlag, New York (1993). [Google Scholar]
  11. I. Karafyllis, P. Pepe and Z.-P. Jiang, Stability Results for Systems Described by Coupled Retarded Functional Differential Equations and Functional Difference Equations. Nonlinear Anal., Theory Methods Appl. 71 (2009) 3339–3362. [CrossRef] [Google Scholar]
  12. I. Karafyllis and Z.-P. Jiang, Stability and Stabilization of Nonlinear Systems. Commun. Control Eng. Springer-Verlag London (2011). [Google Scholar]
  13. I. Karafyllis and M. Krstic, Nonlinear Stabilization under Sampled and Delayed Measurements, and with Inputs Subject to Delay and Zero-Order Hold. IEEE Trans. Autom. Control 57 (2012) 1141–1154. [CrossRef] [Google Scholar]
  14. M. Krstic and A. Smyshlyaev, Backstepping Boundary Control for First-Order Hyperbolic PDEs and Application to Systems With Actuator and Sensor Delays. Syst. Control Lett. 57 (2008) 750–758. [Google Scholar]
  15. M. Krstic, Delay Compensation for Nonlinear, Adaptive, and PDE Systems. Birkhuser Boston (2009). [Google Scholar]
  16. M. Krstic, Input Delay Compensation for Forward Complete and Strict-Feedforward Nonlinear Systems. IEEE Trans. Autom. Control 55 (2010) 287–303. [CrossRef] [Google Scholar]
  17. T.T. Li, Controllability and Observability for Quasilinear Hyperbolic Systems, vol. 3. Higher Education Press, Beijing (2009). [Google Scholar]
  18. D. Melchor-Aguilar, V. Kharitonov and R. Lozano, Stability Conditions for Integral Delay Systems. Int. J. Robust Nonlinear Control 20 2010 1–15. [CrossRef] [Google Scholar]
  19. D. Melchor-Aguilar, On Stability of Integral Delay Systems. Appl. Math. Comput. 217 (2010) 3578–3584. [Google Scholar]
  20. D. Melchor-Aguilar, Exponential Stability of Some Linear Continuous Time Difference Systems. Syst. Control Lett. 61 (2012) 62–68. [Google Scholar]
  21. L. Pavel and L. Chang, Lyapunov-Based Boundary Control for a Class of Hyperbolic Lotka-Volterra Systems. IEEE Trans. Autom. Control 57 (2012) 701–714. [CrossRef] [Google Scholar]
  22. P. Pepe, The Lyapunov’s Second Method for Continuous Time Difference Equations. Int. J. Robust Nonlinear Control 13 (2003) 1389–1405. [CrossRef] [Google Scholar]
  23. C. Prieur and F. Mazenc, ISS-Lyapunov Functions for Time-Varying Hyperbolic Systems of Balance Laws. Math. Control, Signals Syst. 24 (2012) 111–134. [CrossRef] [Google Scholar]
  24. C. Prieur, J. Winkin and G. Bastin, Robust Boundary Control of Systems of Conservation Laws. Math. Control Signals Syst. 20 (2008) 173–197. [CrossRef] [Google Scholar]
  25. V. Rasvan and S.I. Niculescu, Oscillations in Lossless Propagation Models: a Liapunov-Krasovskii Approach. IMA J. Math. Control Inf. 19 (2002) 157–172. [CrossRef] [Google Scholar]
  26. J. Rauch and M. Taylor, Exponential Decay of Solutions to Hyperbolic Equations in Bounded Domains. Indiana University Math. J. 24 (1975). [Google Scholar]
  27. D.L. Russell, Canonical Forms and Spectral Determination for a Class of Hyperbolic Distributed Parameter Control Systems. J. Math. Anal. Appl. 62 (1978) 186–225. [Google Scholar]
  28. D.L. Russell, Neutral FDE Canonical Representations of Hyperbolic Systems. J. Int. Eqs. Appl. 3 (1991) 129–166. [CrossRef] [Google Scholar]
  29. E.D. Sontag, Smooth Stabilization Implies Coprime Factorization. IEEE Trans. Autom. Control 34 (1989) 435–443. [Google Scholar]
  30. R. Vazquez, M. Krstic and J.-M. Coron, Backstepping Boundary Stabilization and State Estimation of a Linear Hyperbolic System, in Proc. of 50th Conf. Decision and Control, Orlando (2011). [Google Scholar]
  31. C.-Z. Xu and G. Sallet, Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems. ESAIM: COCV 7 (2002) 421–442. [CrossRef] [EDP Sciences] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.