A non-interacting control of an r-input m-output linear discrete time system over the lattice group via state variable feedback is considered. In a linear discrete time system over the lattice group, components of the input vector, the output vector and the state vector take only integral values.
This paper defines the sequential reproducibility which corresponds to the functional reproducibility in a linear system over the vector space, and gives a necessary and sufficient condition for the sequential reproducibility in a single-variable linear discrete time system over the lattice group.
This paper defines the non-interacting control system which is sequentially reproducible. A sufficient condition for non-interaction is derived In particular, when r=m, a necessary and sufficient condition for non-interaction is obtained.
General decoupling control laws are given in order to improve responses. An example is given illustrating the result.