Discrete feedback stabilization of semilinear control systems
ESAIM: Control, Optimisation and Calculus of Variations, Volume 1 (1996), pp. 207-224.
@article{COCV_1996__1__207_0,
     author = {Gr\"une, Lars},
     title = {Discrete feedback stabilization of semilinear control systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {207--224},
     publisher = {SMAI (Soci\'et\'e de math\'ematiques appliqu\'ees et industrielles)},
     address = {Paris},
     volume = {1},
     year = {1996},
     mrnumber = {1405041},
     zbl = {0867.93071},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1996__1__207_0/}
}
TY  - JOUR
AU  - Grüne, Lars
TI  - Discrete feedback stabilization of semilinear control systems
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 1996
SP  - 207
EP  - 224
VL  - 1
PB  - SMAI (Société de mathématiques appliquées et industrielles)
PP  - Paris
UR  - http://www.numdam.org/item/COCV_1996__1__207_0/
LA  - en
ID  - COCV_1996__1__207_0
ER  - 
%0 Journal Article
%A Grüne, Lars
%T Discrete feedback stabilization of semilinear control systems
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 1996
%P 207-224
%V 1
%I SMAI (Société de mathématiques appliquées et industrielles)
%C Paris
%U http://www.numdam.org/item/COCV_1996__1__207_0/
%G en
%F COCV_1996__1__207_0
Grüne, Lars. Discrete feedback stabilization of semilinear control systems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 1 (1996), pp. 207-224. http://www.numdam.org/item/COCV_1996__1__207_0/

[1] A. Bacciotti: Local Stabilizability of Nonlinear Control Systems, World Scientific, Singapore, 1992. | MR | Zbl

[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. | MR | Zbl

[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. | Numdam | MR | Zbl

[4] I. Capuzzo Dolcetta and H. Ishii: Approximate solutions of the Bellman equation of deterministic control theory, Appl. Math. Optim., 11, 1984, 161-181. | MR | Zbl

[5] R. Chabour, G. Sallet, and J. Vivalda: Stabilization of nonlinear systems: A bilinear approach, Math. Control Signals Syst., 6, 1993, 224-246. | MR | Zbl

[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.

[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] F. Colonius and W. Kliemann: Linear control semigroups acting on projective space, J. Dyn. Differ. Equations, 5, 1993, 495-528. | MR | Zbl

[9] F. Colonius and W. Kliemann, Maximal and minimal Lyapunov exponents of bilinear control systems, J. Differ. Equations, 101, 1993, 232-275. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[13] L. Grüne: An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation, Numer. Math., 1996. To appear. | MR | Zbl

[14] L. Grüne, Numerical stabilization of bilinear control systems, SIAM J. Control Optim., 1996. To appear. | MR | Zbl

[15] H. Hermes: On stabilizing feedback attitude control, J. Optimization Theory Appl., 31, 1980, 373-384. | MR | Zbl

[16] H. Hermes, On the synthesis of stabilizing feedback control via Lie algebraic methods, SIAM J. Control Optim., 18, 1980, 352-361. | MR | Zbl

[17] A. Isidori: Nonlinear Control systems: An Introduction, Springer Verlag, Berlin, 1989. | MR | Zbl

[18] N.N. Krasovski&Amp;#X012D; and A.I. Subbotin: Game-Theoretical Control Problems, Springer Verlag, New York, 1988. | Zbl

[19] P.-L. Lions: Generalized solutions of Hamilton-Jacobi equations, Pitman, London, 1982. | MR | Zbl

[20] E.D. Sontag: Nonlinear regulation: The piecewise linear approach, IEEE Trans. Autom. Control, AC-26, 1981, 346-358. | MR | Zbl

[21] E.D. Sontag: Feedback stabilization using two-hidden-layer nets, IEEE Trans. Neural Networks, 3, 1992, 981-990.

[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. | MR | Zbl

[23] J. Stoer and R. Bulirsch: Introduction to Numerical Analysis, Springer Verlag, New York, 1980. | MR | Zbl