${\{•\}}_m,{\{•\}}_s$	Subscripts $\left\{m,s\right\}$ denote the master and slave robots, respectively
${\{•\}}_s$	Subscripts s denote the slave robots
$q_i$	Joint position of the master $(i=m)$/slave $(i=s)$ robot in joint space
${\dot{q}}_i$	Joint velocity of the master $(i=m)$/slave $(i=s)$ robot in joint space
${\ddot{q}}_i$	Joint acceleration of the master $(i=m)$/slave $(i=s)$ robot in joint space
${\chi }_i,{\dot{\chi }}_i,{\ddot{\chi }}_i$	Position, velocity, acceleration of the master $(i=m)$/slave $(i=s)$ task-space end effectors
$M_{q_i}(q_i)$	Symmetric positive definite inertia matrix of the master $(i=m)$/slave $(i=s)$ robot in joint space
$M_i(q_i)$	Symmetric positive definite inertia matrix of the master $(i=m)$/slave $(i=s)$ robot in task space
$C_{q_i}(q_i,{\dot{q}}_i){\dot{q}}_i$	Coriolis/centrifugal matrix of the master $(i=m)$/slave $(i=s)$ robot in joint space
$C_i(q_i,{\dot{q}}_i){\dot{q}}_i$	Coriolis/centrifugal matrix of the master $(i=m)$/slave $(i=s)$ robot in task space
$g_{q_i}(q_i)$	Gravitational torque of the master $(i=m)$/slave $(i=s)$ robot in joint space
$g_i(q_i)$	Gravitational torque of the master $(i=m)$/slave $(i=s)$ robot in task space
$f_{q_i}({\dot{q}}_i)$	Viscous friction vector of the master $(i=m)$/slave $(i=s)$ robot in joint space
$f_i({\dot{q}}_i)$	Viscous friction vector of the master $(i=m)$/slave $(i=s)$ robot in task space
$B_{q_i}(q_i)$	Disturbance vector of the master $(i=m)$/slave $(i=s)$ robot in joint space
$B_i(q_i)$	Disturbance vector of the master $(i=m)$/slave $(i=s)$ robot in task space
$F_h,F_e$	Forces exerted on the end-effectors of the master and slave robots by the human operator and environment in joint space, respectively
${\tau }_i(q_i)$	Control torque of the master $(i=m)$ /slave $(i=s)$ robot in joint space
$u_i$	Input control torque of the master $(i=m)$/slave $(i=s)$ robot in task space
$J_i\left(q_i\right)$	Jacobian matrix of the master $(i=m)$/slave $(i=s)$ robot
$T_i$	Time delays from the master robot to the slave robot and from the slave robot to the master robot in task space, respectively
$X_i$	Position and speed state vector set of the master $(i=m)$/slave $(i=s)$ robot in task space
$X_{di}$	Position tracking in task space
${\Theta }_i$	Total disturbance vector of the master $(i=m)$/slave $(i=s)$ robot in task space
$A$	State coefficient matrix in the system equation
$B$	Unknown coefficient matrix in the system equation
$\left\{\overline{•}\right\}$	Discrete form of corresponding coefficient matrix
$\left\{\widetilde{•}\right\}$	The expanded form of the corresponding coefficient matrix
$h$	Sampling time of the master $(i=m)$/slave $(i=s)$ robot in task space
$j$	Jth sampling moment of the master $(i=m)$/slave $(i=s)$ robot in task space
$R$	Real number vector set
$R^n$	N-dimensional real number vector set
$R^{n\times n}$	N-row and n-column real matrix set
$R^{n\times 2n}$	N-row and 2n-column real matrix set
$I$	Identity matrix with appropriate dimensions
${\{•\}}^T$	Superscript T denotes transpose matrix
${\{•\}}^{-1}$	Superscript -1 denotes inverse matrix
$\left\{\widehat{•}\right\}$	Diacritical mark wedge denotes the estimation
$L_{ij}$	Observer gain at the jth sampling time of the master $(i=m)$/slave $(i=s)$ robot in task space
$\alpha ,\beta \dots$	Lowercase Greek letters indicate positive definite constant values
$e_i$	Position synchronization error of the master $(i=m)$/slave $(i=s)$ robot in task space
${\Lambda }_i$	Sliding mode switching parameters of the master $(i=m)$/slave $(i=s)$ robot in task space
$k$	Kth joint in task space
$s_i^{}$	Sliding mode surface of the master $(i=m)$/slave $(i=s)$ robot in task space
$s_i^{{\Delta }_i}$	Sliding surface switching band of the master $(i=m)$/slave $(i=s)$ robot in task space
${\Delta }_i$	Bandwidth of sliding mode surface switching band of the master $(i=m)$/slave $(i=s)$ robot in task space
${\lambda }_i$	Switching gain of sliding surface of the master $(i=m)$/slave $(i=s)$ robot in task space
${\Phi }_i$	Reaching law gain of sliding mode surface of the master $(i=m)$/slave $(i=s)$ robot in task space
$\Vert •\Vert$	Euler norm