A Lyapunov Approach for Discrete-time Sliding Hyperplane Design and Robust Sliding Mode Control using MROF

In this paper, we propose a generalized method to design sliding hyperplane for variable structure control in the discrete time domain. The well-known Lyapunov inequality of full order will be used for generating the stable sliding hyperplanes without loss of generality, which shows the necessary and sufficient condition for the existence of stable sliding hyperplane for multi-input-multi-output systems. Also, we derive a desirable reaching law that guarantees the attractiveness of the boundary layer. Then, it will be shown that the results (obtained with full state feedback information) can be generalized for the discrete time output feedback case by adopting multi-rate output feedback (MROF).