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

Abstract

Summary 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.

Adaptive reaching law‐based discrete‐time sliding mode control for mismatched uncertain systems

“…Theorem 3. For the discrete-time system (4) with sliding surface (6), the DSMC law can be designed by adopting reaching law (7), as follows:…”

“…After the system is driven onto the sliding surface, the system dynamics will be governed by the predesigned sliding surface, and the corresponding state trajectory is called sliding motion, in which matched uncertainties are rejected. 6,7 Since mismatched uncertainties cannot be eliminated through the input channel, the SMC law has the obstacle to forcing sliding mode to occur, which is the reason why SMC fails to deal with mismatched disturbances. 8,9 The mismatched uncertain systems in continuous-time domain have been well studied by a great many of works such as adaptive SMC, 10 linear matrix inequality (LMI) approach, 11 linear/nonlinear observer-based SMC, 12 fuzzy SMC.…”

“…In general, the design of SMC includes two steps: construct a sliding surface with desired static and dynamic properties, and then design SMC laws to force system states to reach the sliding surface. After the system is driven onto the sliding surface, the system dynamics will be governed by the predesigned sliding surface, and the corresponding state trajectory is called sliding motion, in which matched uncertainties are rejected 6,7 …”