A Non-singular Terminal Recursive Surface Structure Design for Higher-order Systems

In this paper, the idea behind recursive surface structure design is further investigated for an arbitrary-order system. The sliding mode control is formulated for single-input single-output dynamical systems in the chain-of-integrator form. Terminal surfaces usually lead to singularity in control. Some of the methods are proposed in the past dealing with the aforementioned issue. This paper further investigates the elimination of singularity condition while preserving the terminal structure, leading to finite-time convergence during sliding. The conditions to ensure its applicability for singularity free control design are derived. It is interesting to find that the conditions obtained in the proposed case is similar to that of Fast Terminal Sliding-Mode (FTSM) control design. Therefore, it can be suggested that the FTSM surface structure can be modified to the proposed form in order to get the equivalent convergence speed while alleviating the singularity in control.