On exponential stabilisation for descriptor time-delay systems with nonlinear input via SMC

The problem of exponential stabilisation for a class of uncertain descriptor time-delay systems (DTS) is investigated, where both nonlinear input and external disturbance are involved. A novel sliding mode control (SMC) scheme is developed to achieve a stable uncertain system. A delay-free linear sliding surface is first introduced for control design of the DTS. A new adaptive controller is designed to ensure the state trajectories globally to converge onto the sliding surface. Furthermore, the considered sliding mode dynamics (SMDs) are derived via equivalent control of the SMC, once the system is in the sliding mode, the proposed criterion can guarantee the SMDs to be exponentially admissible and passive. Finally, the effectiveness of the proposed scheme is verified via an example.