An LMI-based finite-time tracker design using nonlinear sliding surfaces

This paper offers a new nonlinear sliding surface to achieve robustness and high performance for uncertain MIMO linear systems. The proposed method improves the transient performance and steady state accuracy simultaneously in a finite time. Exponential boundedness and ultimately boundedness conditions in finite time are provided in the form of linear matrix inequalities (LMIs). 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. 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 way for controlling similar nonlinear systems.