Multiplexed order-reducing control of linear discrete-time systems

In this work we consider linear discrete-time systems for which groups of control inputs are updated sequentially and cyclically instead of simultaneously, in what is called a multiplexed implementation. Such update scheme may arise, for instance, when hardware or computational constraints make impossible the simultaneous update of all actuators. A control law is proposed here for asymptotic stabilization of the resulting periodic system by the introduction of a set of subspaces to which the system state is driven, resembling sliding mode techniques. The applicability of the method includes systems which are not stabilizable from the update groups of actuators if taken individually. Simulations with a marginally stable system demonstrate the method.