# Specific discrete system $x_n = A(n,u)\cdot x_{n-1}$ control papers

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?

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), for which optimal control results have appeared in literature.