  A novel control method is proposed to ensure compatibility of safe,
stabilizing control laws, i.e., simultaneous satisfaction of asymptotic
stability and constraint satisfaction for nonlinear affine systems. The results
are dependent on an asymptotically stabilizing control law and a zeroing
control barrier function (ZCBF), but do not require a control Lyapunov function
(CLF). Sufficient conditions for a region of attraction are defined for which
the proposed control safely stabilizes the system, while preserving the
decrescent Lyapunov function of the original stabilizing control law. The
proposed methodology for nonlinear affine systems requires checking conditions
of the system dynamics over a substantial portion of the state space, which may
be computationally expensive. To facilitate the search for compatibility, we
extend the results to a class of nonlinear systems including mechanical systems
for which a novel controller is designed to guarantee passivity, safety, and
stability. Numerical examples are used to demonstrate the proposed technique.
