Optimal discrete systems with pure delays

Necessary and sufficient conditions for the optimization of multivariable discrete systems containing pure delays in dynamics, in performance index, and in constraints are investigated. Using nonlinear programming, it is shown that a discrete maximum principle similar to the one derived by Pearson and Sridhar [1] is valid for a subclass of these problems, that is, systems with linear dynamics, convex inequality constraints, and convex performance index.