In order to enhance the convergence rate of NTSM (3), a new FNTSM is designed as
The FNTSM (6) is a switching sliding surface which transfers the system dynamic from a LSM (q = l) toa NTSM (l < q < 2) (Figure 1; e.
Here, a simple example is given to compare the NTSM (3) and the FNTSM (6),
Considering system (7), the control input was taken as the NTSM controller form of 
Note that the FNTSM became equivalent to the NTSM within the region [absolute value of [x.
Most of the NTSM controllers were designed for system (1) with a known y (or with an uncertain item).
Generally, the NTSM control design contains the sliding surface and the reaching law.
2]) in the existing NTSM controllers, for example, the controller (8).
In the studies of adaptive NTSM control [22, 23], the switching gain was directly adjusted by the adaptive technique.
In this section, a double sliding surfaces control scheme is designed to combine the NTSM control with the adaptive technique.
Although the proposed NTSM controller (11) in Theorem 2 can be used to design [u.
In this section, the designed robust and adaptive NTSM controllers were tested for the tracking control of a variable-length pendulum  (Figure 3) formulated as