Global sliding mode control for uncertain linear systems with state time-delays

The problem of designing global sliding mode controllers for a class of linear and uncertain systems with time delays of state was concerned. Firstly, A nonsingular linear transformation was defined. The original system with state time-delays was rewritten into a form without any time-delays by this nonsingular linear transformation. We proposed a new method for integral sliding surface. It can make up for the deficiencies of the traditional sliding surface, eliminating the process of reaching and ensuring the global robustness of the system. Secondly, the sliding mode controller was designed based on the transformed system. It ensures that all trajectories starting off the manifold reach it in finite time and have low chattering in the sliding motion. A sufficient asymptotic stability condition of the original system was proposed. Finally, the efficiency and superiority of the proposed method were demonstrated by simulation study.