A new discrete-time sliding-mode control with time-varying gain and neural identification

In this paper, we present a new sliding mode controller for a class of unknown non-linear discrete-time systems. We make the following two modifications. (1) The neural identifier which is used to estimate the unknown non-linear system uses the projection and the dead-zone approaches to assure non-singularity in the controller and stability of identification error. (2) We propose a new sliding mode controller with time-varying gain to reduce chattering. A necessary condition is given to make the switching function decrease exponentially. We prove that the closed-loop system with the sliding mode controller and the neural identifier is stable.