Discrete-time systems sliding mode switching hyperplane design: A survey

As regards to variable structure control with sliding mode (VSC-SM), it is known that designing sliding surface is a critical task because sliding surfaces must guarantee that the steady state of the controlled system achieves some desired performance including global (or global asymptotic) stability. This problem has been extensively analyzed for a wide class of systems: scalar, multivariable, linear, nonlinear, time-variant, discrete-time system, etc. The main purpose of this paper is to present a thorough survey about the main approaches related to the design of discrete-time switching surfaces applied to VSC-SM. Research works covering the design of sliding surfaces for the aforementioned systems are considered and some illustrative examples are also included to explain some of the design methodologies.