H2 optimization for systems with adobe input delays: A loop shifting approach

This paper studies the H2 optimization problem for systems with adobe input delay. These are systems having only two (possibly vector) input channels: one is delay free and the other is delayed. We present a solution based on the reduction of the problem to an equivalent delay-free problem via simple loop shifting arguments. This results in a solution based on two standard algebraic Riccati equations, which are associated with the delay-free version of the problem. The optimal controller is in the dead-time compensator form. We also derive an explicit and transparent expression for the cost of delay and (in the case when the problem is solvable without the delayed channel) a numerically stable form of the optimal solution, which includes exponentials of Hurwitz matrices only. The approach is readily extendible to more general multiple input / output delay cases.