Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 255-263 |
| Number of pages | 9 |
| Journal | Systems and Control Letters |
| Volume | 21 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 1993 |
Keywords
- Discrete-time nonlinear systems
- critical problems of stabilization
- linear approximation
- local and global asymptotic stabilization
- smooth state feedback
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Byrnes, C. I., Lin, W., & Ghosh, B. K. (1993). Stabilization of discrete-time nonlinear systems by smooth state feedback. Systems and Control Letters, 21(3), 255-263. https://doi.org/10.1016/0167-6911(93)90036-6