TY - JOUR
T1 - Stabilization of discrete-time nonlinear systems by smooth state feedback
AU - Byrnes, Christopher I.
AU - Lin, Wei
AU - Ghosh, Bijoy K.
N1 - Funding Information:
Correspondence to: C.I. Byrnes, Department of Systems Science and Mathematics, Washington University, St. Louis, MO 63130, USA * Research supported in part by grants from the AFOSR and NSF.
PY - 1993/9
Y1 - 1993/9
N2 - For a class of nonlinear discrete-time systems of the form Σ: x(k+1)=f{hook}(x(k))+g(x(k))u(k), we investigate conditions under which a nonlinear system can be rendered globally asymptotically stable via smooth state feedback. Our main result is that any nonlinear system with Lyapunov-stable unforced dynamics can always be globally stabilized by smooth state feedback if suitable controllability-like rank conditions are satisfied. Several examples are presented to demonstrate the applications of the stability results developed in this paper.
AB - For a class of nonlinear discrete-time systems of the form Σ: x(k+1)=f{hook}(x(k))+g(x(k))u(k), we investigate conditions under which a nonlinear system can be rendered globally asymptotically stable via smooth state feedback. Our main result is that any nonlinear system with Lyapunov-stable unforced dynamics can always be globally stabilized by smooth state feedback if suitable controllability-like rank conditions are satisfied. Several examples are presented to demonstrate the applications of the stability results developed in this paper.
KW - Discrete-time nonlinear systems
KW - critical problems of stabilization
KW - linear approximation
KW - local and global asymptotic stabilization
KW - smooth state feedback
UR - http://www.scopus.com/inward/record.url?scp=0027656970&partnerID=8YFLogxK
U2 - 10.1016/0167-6911(93)90036-6
DO - 10.1016/0167-6911(93)90036-6
M3 - Article
AN - SCOPUS:0027656970
VL - 21
SP - 255
EP - 263
JO - Systems and Control Letters
JF - Systems and Control Letters
SN - 0167-6911
IS - 3
ER -