A Geometric Approach to Feedback Stabilization of Nonlinear Systems with Drift

Abstract

The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous state feedback. The approach is independent of the selection of a Lyapunov type function, but requires the solution of a nonlinear programming 'satisficing problem' stated in terms of the logarithmic coordinates of flows. As opposed to other approaches, point-to-point steering is not required to achieve asymptotic stability. Instead, the flow of the controlled system is required to intersect periodically a certain reachable set in the space of the logarithmic coordinates.