We study the leader-following consensus stability and stabilization of networked multi-teleoperator systems with interval time-varying communication delays. With the construction of a suitable Lyapunov-Krasovskii functional and the utilization of the reciprocally convex approach, novel delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities, which can easily be solved by various effective optimization algorithms. One illustrative example is given to illustrate the effectiveness of the proposed methods. We study the leader-following consensus stability and stabilization of networked multi-teleoperator systems with interval time-varying communication delays. With the construction of a suitable Lyapunov-Krasovskii functional and the utilization of the reciprocally convex approach, novel delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities, which can easily be solved by various effective optimization algorithms. One illustrative example is given to illustrate the effectiveness of the proposed methods.