Abstract
For a class of nonlinear discrete-time systems of the form Σ: x(k+1)=ƒ(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.
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