Basic discrete control theory mostly studies systems which can be represented as $x\_n=A(n)x\_{n-1}+B(n)u\_n$.


I wonder if optimal control of specific discrete systems of the type $x\_n = A(n,u)\cdot x\_{n-1}$ have been described in any paper?


Or maybe there is a control theory handbook where different systems and their presumed control are listed?



Specific discrete system $x_n = A(n,u)\cdot x_{n-1}$ control papers
If you are willing to consider the special case that $A(n,u)$ is linear in control $u$, then this becomes a bilinear control system (see for example, [the book by David Elliott](http://www.springer.com/us/book/9781402096129?token=prtst0416p)), for which optimal control results have appeared in literature.


