Abstract: This paper considers the problem of designing a controller that simultaneously stabilizes a
collection of multi-input nonlinear systems. Based on the technique of control Lyapunov function, a
sufficient condition for the existence of time-invariant simultaneously stabilizing state feedback controller
is obtained. A universal formula for constructing a continuous controller which simultaneously stabilizes
the systems is derived. The result extends the existing one in [1] for the single-input case.

Key words: simultaneous stabilization, affine nonlinear system, control Lyapunov function, state feedback