An LMI‐based composite nonlinear feedback terminal sliding‐mode controller design for disturbed MIMO systems

This paper proposes a new nonlinear sliding surface for a terminal sliding mode (TSM) controller to achieve robustness and high performance tracking for the disturbed MIMO systems. The proposed method improves the transient performance and steady state accuracy in a finite time simultaneously. The control law is designed to guarantee the existence of the sliding mode around the nonlinear surface, and the damping ratio of the closed‐loop system is increased as the output approaches the set‐point. The conditions on the state error bound in finite time are expressed in the form of linear matrix inequalities (LMIs). A DC motor position tracking problem is considered as a case study. Simulation results are presented to show the effectiveness of the proposed method as a promising approach for controlling similar nonlinear systems.