  We present a novel approach that aims to address both safety and stability of
a haptic teleoperation system within a framework of Haptic Shared Autonomy
(HSA). We use Control Barrier Functions (CBFs) to generate the control input
that follows the user's input as closely as possible while guaranteeing safety.
In the context of stability of the human-in-the-loop system, we limit the force
feedback perceived by the user via a small $L_2$-gain, which is achieved by
limiting the control and the force feedback via a differential constraint.
Specifically, with the property of HSA, we propose two pathways to design the
control and the force feedback: Sequential Control Force (SCF) and Joint
Control Force (JCF). Both designs can achieve safety and stability but with
different responses to the user's commands. We conducted experimental
simulations to evaluate and investigate the properties of the designed methods.
We also tested the proposed method on a physical quadrotor UAV and a haptic
interface.
