ABSTRACT
A robust LMI-based method is developed for the design of discrete-time sliding mode control (DSMC) for uncertain systems. The proposed robust DSMC can be applied to unstable systems, and also there is no need to stabilize the underlying system first. It is also shown that with the assumption of smoothness of the external disturbances, a different form of switching element in the controller can outperform the so-called linear controller in terms of the thickness of the boundary layer around the sliding function and the ultimate bound on the system state. Furthermore, the idea of disturbance estimation is extended to uncertain discrete-time systems. In continuous-time sliding mode control, to achieve ideal sliding mode, in general the control signal must switch at infinite frequency. This chapter explains a more practical DSMC for the systems including uncertainty and disturbance. Effectiveness of the proposed DSMC is studied by numerical examples.
