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

Authors:
L. Mirkin;Z. J. Palmor;D. Shneiderman
Affiliations:
-;-;-
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

This paper studies the H^2 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.