Dynamic Behavior of Terminal Sliding Mode Control

This paper proposes two new definitions and related theorems in analyzing the transient behavior of terminal sliding mode control (TSMC) for nonlinear systems. The first one is named critical trajectory (CT), which is used to characterize the system dynamics for both TSMC and its nonsingular version, i.e., nonsingular TSMC (NTSMC). The second one is named constrained surface (CS), which is used to characterize the phase trajectory for NTSMC. Based on these two terms, we further propose two new theorems and their associated rigorous proofs that can be used to comprehensively describe the dynamic behavior of TSMC and NTSMC. In addition to theoretical analyses, we also present two case studies, i.e., one numerical example and one two-link manipulator system, to verify the effectiveness of the proposed theoretical research.