Discrete feedback stabilization of semilinear control systems

Lars Grüne

ESAIM: Control, Optimisation and Calculus of Variations (1996)

  • Volume: 1, page 207-224
  • ISSN: 1292-8119

How to cite


Grüne, Lars. "Discrete feedback stabilization of semilinear control systems." ESAIM: Control, Optimisation and Calculus of Variations 1 (1996): 207-224. <http://eudml.org/doc/90496>.

author = {Grüne, Lars},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {stabilization; exponential stabilizability; discounted optimal control; piecewise constant control},
language = {eng},
pages = {207-224},
publisher = {EDP Sciences},
title = {Discrete feedback stabilization of semilinear control systems},
url = {http://eudml.org/doc/90496},
volume = {1},
year = {1996},

AU - Grüne, Lars
TI - Discrete feedback stabilization of semilinear control systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1996
PB - EDP Sciences
VL - 1
SP - 207
EP - 224
LA - eng
KW - stabilization; exponential stabilizability; discounted optimal control; piecewise constant control
UR - http://eudml.org/doc/90496
ER -


  1. [1] A. Bacciotti: Local Stabilizability of Nonlinear Control Systems, World Scientific, Singapore, 1992. Zbl0757.93061MR1148363
  2. [2] R.W. Brockett: Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory, R.W. Brockett, R.S. Millman, and H.J. Sussmann, eds., 181-191, Birkhäuser, Boston, 1983. Zbl0528.93051MR708502
  3. [3] I. Capuzzo Dolcetta and M. Falcone: Discrete dynamic programming and viscosity solutions of the Bellman equation, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 6 (supplément), 1989, 161-184. Zbl0674.49028MR1019113
  4. [4] I. Capuzzo Dolcetta and H. Ishii: Approximate solutions of the Bellman equation of deterministic control theory, Appl. Math. Optim., 11, 1984, 161-181. Zbl0553.49024MR743925
  5. [5] R. Chabour, G. Sallet, and J. Vivalda: Stabilization of nonlinear systems: A bilinear approach, Math. Control Signals Syst., 6, 1993, 224-246. Zbl0797.93038MR1358071
  6. [6] F. Clarke, Y. Ledyaev, E. Sontag, and A. Subbotin: Asymptotic controllability and feedback stabilization, in Proc. Conf. on Information Sciences and Systems (CISS 96), Princeton, NJ, 1996. To appear, full version submitted. Zbl0892.93053
  7. [7] B. D. Coller, P. Holmes, and J. L. Lumley: Control of bursting in boundary layer models, Appl. Mech. Rev., 47, 1994, 139-143. 
  8. [8] F. Colonius and W. Kliemann: Linear control semigroups acting on projective space, J. Dyn. Differ. Equations, 5, 1993, 495-528. Zbl0784.34049MR1235040
  9. [9] F. Colonius and W. Kliemann, Maximal and minimal Lyapunov exponents of bilinear control systems, J. Differ. Equations, 101, 1993, 232-275. Zbl0769.34037MR1204328
  10. [10] F. Colonius and W. Kliemann, Asymptotic null controllability of bilinear systems, in Geometry in Nonlinear Control and Differential Inclusions, Banach Center Publications Vol. 32, Warsaw, 1995, 139-148. Zbl0837.93050MR1364425
  11. [11] M. Falcone: A numerical approach to the infinite horizon problem of deterministic control theory, Appl. Math. Optim., 15, 1987, 1-13. Corrigenda, ibid. 23, 1991, 213-214. Zbl0715.49025MR866164
  12. [12] M. Falcone and R. Ferretti: Discrete time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations, Numer. Math., 67, 1994, 315-344. Zbl0791.65046MR1269500
  13. [13] L. Grüne: An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation, Numer. Math., 1996. To appear. Zbl0880.65045MR1427711
  14. [14] L. Grüne, Numerical stabilization of bilinear control systems, SIAM J. Control Optim., 1996. To appear. Zbl0876.93032MR1416498
  15. [15] H. Hermes: On stabilizing feedback attitude control, J. Optimization Theory Appl., 31, 1980, 373-384. Zbl0417.93060MR600064
  16. [16] H. Hermes, On the synthesis of stabilizing feedback control via Lie algebraic methods, SIAM J. Control Optim., 18, 1980, 352-361. Zbl0477.93046MR579546
  17. [17] A. Isidori: Nonlinear Control systems: An Introduction, Springer Verlag, Berlin, 1989. Zbl0569.93034MR1229759
  18. [18] N.N. Krasovski&#x012D; and A.I. Subbotin: Game-Theoretical Control Problems, Springer Verlag, New York, 1988. Zbl0649.90101
  19. [19] P.-L. Lions: Generalized solutions of Hamilton-Jacobi equations, Pitman, London, 1982. Zbl0497.35001MR667669
  20. [20] E.D. Sontag: Nonlinear regulation: The piecewise linear approach, IEEE Trans. Autom. Control, AC-26, 1981, 346-358. Zbl0474.93039MR613541
  21. [21] E.D. Sontag: Feedback stabilization using two-hidden-layer nets, IEEE Trans. Neural Networks, 3, 1992, 981-990. 
  22. [22] N. Sri Namachchivaya and H.J. Van Roessel: Maximal Lyapunov exponents and rotation numbers for two coupled oscillators driven by real noise, J. Stat. Phys., 71, 1993, 549-567. Zbl0945.60503MR1219022
  23. [23] J. Stoer and R. Bulirsch: Introduction to Numerical Analysis, Springer Verlag, New York, 1980. Zbl0423.65002MR557543

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