On LMI-based sliding mode control for uncertain discrete-time systems

In this paper, a new approach to design a robust discrete-time sliding mode control (DSMC) is proposed for uncertain discrete-time systems. To this end, an LMI approach is used to develop a new framework to design the sliding function which is linear to the state. Our proposed robust DSMC can be applied to unstable systems, and also there is no need to stabilize the underlying system first. It has been argued in the literature that for the systems involving balanced external disturbances, using switching component is not needed. In this paper, it is 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. Also, this paper extends the idea of disturbance estimation to the uncertain discrete-time systems. The disturbance estimator is exploited in the controller design and the boundedness of the obtained closed-loop system is analyzed. Also, two novel forms of variable structure DSMC are suggested in this paper.