Pole-placement in discrete systems by using single and multirate sampling

This paper deals with closed-loop pole-placement in discrete, linear systems under single and multirate sampling. The technique is extendable to hybrid systems, i.e. those involving both continuous and discrete substates. The sampling rates for the state, input and output components are used as a controller design technique to achieve closed-loop pole-placement since the controller, which is also discrete or hybrid in the general case, can be periodically reparametrized, the main useful effect of which being the availability of multiple design gains whose number and value are under the designer's choice. The key design factor in the multirate sampling design is that once the closed-loop running sampling period (i.e. that defining the closed-loop dynamics and thus the controller reparametrization periodicity) has been chosen, one can use freedom in the choice of smaller sampling periods for the various plant input and output components as well as for those of the controller state. All these sampling periods are chosen as submultiples of the closed-loop running sampling period.