Discrete-time VS controller design based on input-output model

Variable structure control (VSC) methods are generally based on the state space model. To implement the VSC in practical systems, all state variables should be measurable otherwise an observer or some other algorithm should be used to estimate the unmeasurable state variables. In the paper, the discrete-time VS controller with sliding sector, which results in a quadratic stable VS control system in state space is redesigned with input-output model of the considered discrete-time system. The control law is represented by past input and output, and therefore can be implemented in those discrete-time systems where the input and output variables are measurable