BOUNDED SMOOTH STATE-FEEDBACK AND A GLOBAL SEPARATION PRINCIPLE FOR NON-AFFINE NONLINEAR-SYSTEMS

In this paper we show that a single-input nonlinear system Sigma: x = f(0)(x)+g(1)(x)u+... g(l)(x)u(l) is globally asymptotically stabilizable by al bituarily small smooth state feedback if unforced dynamics of Sigma are Lyapunov stable and Sigma satisfies appropriate controllability-like rank conditions characterized by the Lie bracket of vector fields f(0)(x) and g(1)(x). An explicit smooth state feedback control law is constructed. This, in turn, leads to an analytic (resp. smooth) state feedback control law which solves the problem of global stabilization for analytic (resp. smooth) systems x = f(x,u). Based on these results, we then establish a global separation principle for the system Sigma with an output. Finally, we briefly discuss how the results can be extended to a multi-input system.