Design of funnel function-based discrete-time sliding mode control

This study presents the design and analysis of a novel funnel function-based sliding mode reaching law for uncertain discrete-time systems. The presented reaching law is featured by the funnel function, which is established on the basis of the switching function, and the perturbation estimation technique. As compared with previous researches, the developed method is capable of regulating both transient and steady-state performance. The system trajectory can be maintained within a predefined boundary, i.e. the desired limit of the trajectory evolution, described by the funnel function in the presence of disturbances. Theoretical analyses confirm the convergence and boundedness of the controlled system. A practical verification example is given to demonstrate the validity of the presented method.