Simultaneous stabilization for a collection of single-input nonlinear systems

This paper presents a novel method for designing a controller that simultaneously stabilizes a collection of single-input nonlinear systems. The control Lyapunov function approach is used to derive necessary and sufficient conditions for the existence of time-invariant simultaneously stabilizing state feedback controllers. Additionally, a universal formula for constructing a continuous simultaneously stabilizing controller when the provided sufficient condition is satisfied is presented. For any collection of second-order (and third-order) feedback linearizable systems in canonical form, global simultaneous stabilization via a single state feedback controller is shown to be always possible. Two examples are included for illustration.