Sufficient conditions for the simultaneous stabilizability of nonlinear systems

The simultaneous stabilization of a finite family of control systems consists in finding a feedback law that asymptotically stabilizes all the systems in the family. In this paper, we derive sufficient conditions for the existence of a continuous time-varying feedback law that simultaneously locally or globally asymptotically stabilizes a finite family of nonlinear systems. We then focus on certain pairs of nonlinear homogeneous systems, and by using the obtained sufficient conditions, we establish their asymptotic stabilizability by means of time-varying feedback