EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 12 / No 1 (January 2006) ESAIM: COCV, 12 1 (2006) 169-197 References
Free Access

This article has an erratum: [https://doi.org/10.1051/cocv/2009011]

Issue
ESAIM: COCV
Volume 12, Number 1, January 2006
Page(s) 169 - 197
DOI https://doi.org/10.1051/cocv:2005027
Published online 15 December 2005
  1. W. Arendt and C.J.K. Batty, Tauberian theorems and stability of one-parameter semigroups. Trans. Amer. Math. Soc. 306 (1988) 837–852. [CrossRef] [MathSciNet] [Google Scholar]
  2. A.V. Balakrishnan, On a generalization of the Kalman-Yacubovic lemma. Appl. Math. Optim. 31 (1995) 177–187. [CrossRef] [MathSciNet] [Google Scholar]
  3. F. Bucci, Frequency domain stability of nonlinear feedback systems with unbounded input operator. Dynam. Contin. Discrete Impuls. Syst. 7 (2000) 351–368. [Google Scholar]
  4. F.M. Callier and J. Winkin, LQ-optimal control of infinite-dimensional systems by spectral factorization. Automatica 28 (1992) 757–770. [CrossRef] [MathSciNet] [Google Scholar]
  5. R.F. Curtain, Linear operator inequalities for strongly stable weakly regular linear systems. Math. Control Signals Syst. 14 (2001) 299–337. [CrossRef] [Google Scholar]
  6. R.F. Curtain, Regular linear systems and their reciprocals: application to Riccati equations. Syst. Control Lett. 49 (2003) 81–89. [CrossRef] [Google Scholar]
  7. R.F. Curtain, Riccati equations for stable well-posed linear systems: The generic case. SIAM J. Control Optim. 42 (2003) 1671–1702. [Google Scholar]
  8. R.F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory. Heidelberg, Springer (1995). [Google Scholar]
  9. R.F. Curtain, H. Logemann and O. Staffans, Stability results of Popov-type for infinite – dimensional systems with applications to integral control. Proc. London Math. Soc. 86 (2003) 779–816. [CrossRef] [MathSciNet] [Google Scholar]
  10. H. Górecki, S. Fuksa, P. Grabowski and A.Korytowski, Analysis and Synthesis of Time-Delay Systems. Warsaw & Chichester: PWN and J. Wiley (1989). [Google Scholar]
  11. P. Grabowski, On the spectral – Lyapunov approach to parametric optimization of DPS. IMA J. Math. Control Inform. 7 (1990) 317–338. [CrossRef] [MathSciNet] [Google Scholar]
  12. P. Grabowski, The LQ controller problem: an example. IMA J. Math. Control Inform. 11 (1994) 355–368. [CrossRef] [MathSciNet] [Google Scholar]
  13. P. Grabowski, On the circle criterion for boundary control systems in factor form. Opuscula Math. 23 (2003) 1–25. [Google Scholar]
  14. P. Grabowski and F.M. Callier, Admissible observation operators. Duality of observation and control using factorizations. Dynamics Continuous, Discrete Impulsive Systems 6 (1999) 87–119. [Google Scholar]
  15. P. Grabowski and F.M. Callier, On the circle criterion for boundary control systems in factor form: Lyapunov approach. Facultés Universitaires Notre-Dame de la Paix à Namur, Publications du Département de Mathématique, Research Report 07 (2000), FUNDP, Namur, Belgium. [Google Scholar]
  16. P. Grabowski and F.M. Callier, Boundary control systems in factor form: Transfer functions and input-output maps. Integral Equations Operator Theory 41 (2001) 1–37. [CrossRef] [MathSciNet] [Google Scholar]
  17. P. Grabowski and F.M. Callier, Circle criterion and boundary control systems in factor form: Input-output approach. Internat. J. Appl. Math. Comput. Sci. 11 (2001) 1387–1403. [Google Scholar]
  18. P. Grabowski and F.M. Callier, On the circle criterion for boundary control systems in factor form: Lyapunov stability and Lur'e equations. Facultés Universitaires Notre-Dame de la Paix à Namur, Publications du Département de Mathématique, Research Report 05 (2002), FUNDP, Namur, Belgium. [Google Scholar]
  19. U. Grenander and G. Szegö, Toeplitz Forms and Their Application, Berkeley: University of California Press (1958). [Google Scholar]
  20. K. Hoffman, Banach Spaces of Analytic Functions. Englewood Cliffs: Prentice-Hall (1962). [Google Scholar]
  21. I. Lasiecka and R. Triggiani, Differential and Algebraic Riccati Equations with Application to Boundary/Point Control Problems: Continuous Theory and Approximation Theory. Lect. Notes Control Inform. Sci. 164 (1991) 1–160. [CrossRef] [Google Scholar]
  22. I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations: Continuous and Approximation Theories. Part I: Abstract Parabolic Systems, Cambridge: Cambridge University Press, Encyclopedia Math. Appl. 74 (2000). [Google Scholar]
  23. I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations: Continuous and Approximation Theories. Part II: Abstract Hyperbolic-Like Systems over a Finite Time Horizon, Cambridge: Cambridge University Press, Encyclopedia Math. Appl. 75 (2000). [Google Scholar]
  24. A.L. Likhtarnikov and V.A. Yacubovich, The frequency domain theorem for continuous one-parameter semigroups, IZVESTIJA ANSSSR. Seria matematicheskaya. 41 (1977) 895–911 (in Russian). [Google Scholar]
  25. H. Logemann and R.F. Curtain, Absolute stability results for well-posed infinite-dimensional systems with low-gain integral control. ESAIM: COCV 5 (2000) 395–424. [CrossRef] [EDP Sciences] [Google Scholar]
  26. J.-Cl. Louis and D.Wexler, The Hilbert space regulator problem and operator Riccati equation under stabilizability. Annales de la Société Scientifique de Bruxelles 105 (1991) 137–165. [Google Scholar]
  27. Yu. Lyubich and Vû Quôc Phong, Asymptotic stability of linear differential equations in Banach spaces. Studia Math. 88 (1988) 37–41. [MathSciNet] [Google Scholar]
  28. E. Noldus, On the stability of systems having several equilibrium points. Appl. Sci. Res. 21 (1969) 218–233. [CrossRef] [Google Scholar]
  29. E. Noldus, A. Galle and L. Jasson, The computation of stability regions for systems with many singular points. Intern. J. Control 17 (1973) 641–652. [CrossRef] [Google Scholar]
  30. E. Noldus, New direct Lyapunov-type method for studying synchronization problems. Automatica 13 (1977) 139–151. [CrossRef] [MathSciNet] [Google Scholar]
  31. A.A. Nudel'man and P.A. Schwartzman, On the existence of solution of some operator inequalities. Sibirsk. Mat. Zh. 16 (1975) 563–571 (in Russian). [Google Scholar]
  32. J.C. Oostveen and R.F. Curtain, Riccati equations for strongly stabilizable bounded linear systems. Automatica 34 (1998) 953–967. [CrossRef] [MathSciNet] [Google Scholar]
  33. L. Pandolfi, Kalman-Popov-Yacubovich theorem: an overview and new results for hyperbolic control systems. Nonlinear Anal. Theor. Methods Appl. 30 (1997) 735–745. [CrossRef] [Google Scholar]
  34. L. Pandolfi, Dissipativity and Lur'e problem for parabolic boundary control system, Research Report, Dipartamento di Matematica, Politecnico di Torino 1 (1997) 1–27; SIAM J. Control Optim. 36 (1998) 2061–2081. [Google Scholar]
  35. L. Pandolfi, The Kalman-Yacubovich-Popov theorem for stabilizable hyperbolic boundary control systems. Integral Equations Operator Theory 34 (1999) 478–493. [CrossRef] [MathSciNet] [Google Scholar]
  36. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. New York, Springer-Verlag (1983). [Google Scholar]
  37. D. Salamon, Realization theory in Hilbert space. Math. Systems Theory 21 (1989) 147–164. [CrossRef] [MathSciNet] [Google Scholar]
  38. O.J. Staffans, Quadratic optimal control of stable well-posed linear systems through spectral factorization. Math. Control Signals Systems 8 (1995) 167–197. [CrossRef] [MathSciNet] [Google Scholar]
  39. O.J. Staffans and G. Weiss, Transfer functions of regular linear systems, Part II: The system operator and the Lax-Phillips semigroup. Trans. Amer. Math. Soc. 354 (2002) 3229–3262. [CrossRef] [MathSciNet] [Google Scholar]
  40. M. Vidyasagar, Nonlinear Systems Analysis. 2nd Edition, Englewood Cliffs NJ, Prentice-Hall (1993). [Google Scholar]
  41. G. Weiss, Transfer functions of regular linear systems. Part I: Characterization of regularity. Trans. AMS 342 (1994) 827–854. [Google Scholar]
  42. M. Weiss, Riccati Equations in Hilbert Spaces: A Popov function approach. Ph.D. Thesis, Rijksuniversiteit Groningen, The Netherlands (1994). [Google Scholar]
  43. M. Weiss and G. Weiss, Optimal control of stable weakly regular linear systems. Math. Control Signals Syst. 10 (1997) 287–330. [CrossRef] [Google Scholar]
  44. R.M. Young, An Introduction to Nonharmonic Fourier Series. New York, Academic Press (1980). [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.