Global robust sliding mode control for a class of uncertain time-delay systems

A global robust sliding mode controller (GRSMC) is proposed for a class of uncertain systems with both state-delay and input-delay. Firstly, a linear transformation is introduced to transform the original system into one that only contains state-delay. Then an integral sliding mode surface, which can guarantee the system global robustness, is constructed in the new system of coordinates. Based on linear matrix inequality (LMI), a sufficient condition that ensures asymptotic stability of the sliding mode is derived, and furthermore the asymptotic stability of the original system is studied. A sliding mode control law is designed to satisfy the reaching condition of the sliding mode. So a GRSMC is realized. Finally, the effectiveness of the proposed method is demonstrated by applying to a networked control system with network-induced time delays.