Non-Smooth Simultaneous Stabilization of Nonlinear Systems: Interpolation of Feedback Laws

Abstract

In this paper, we introduce a method that enables us to construct a continuous simultaneous stabilizer for pairs of systems in the plane that cannot be simultaneously stabilized by smooth feedback. We extend this method to higher dimensional systems and prove that any pair of asymptotically stabilizable nonlinear systems can be simultaneously stabilized (not asymptotically) by means of continuous feedback. The resulting simultaneous stabilizer depends on a partition of unity and we show how to circumvent the computation of this partition of unity by constructing an explicit simultaneous stabilizer.