Multivariable system stabilization via discrete variable structure control

•A Generalized Minimum Variance Multivariable Control (VSC/GMV) with interactor matrix synthesis is presented.•A precompensator design, to overcome multivariable (MIMO) plants with coupling has also been developed.•Simulations results are presented to validate the potentiality of discrete MIMO VSC/GMV controller.•Numerical simulations with processes that presents distinct response speeds and control coupling levels are presented.

This paper presents the design of an incremental discrete variable structure controller, based on the minimization of the generalized minimum variance approach, to deal with multivariable plants and to handle different time delay of control loops between the input–output pairs. Additionally, a static precompensator, to decouple the control loops in multivariable systems, is developed not only to keep a good closed-loop behavior but also to decrease the control algorithm complexity. Numerical simulation examples are shown to illustrate the dynamic performance and the closed-loop stability for three multivariable systems.