The H2 Control Problem for Quadratically Invariant Systems with Delays

TL;DR

This paper presents a novel convex approach to the output feedback H2 control problem for systems with communication delays, providing a finite-dimensional quadratic program solution and a recursive state-space computation method.

Contribution

It introduces a new convex formulation for the H2 control problem under delay constraints and offers a recursive state-space method for optimal controller computation.

Findings

The control problem can be reduced to a finite-dimensional quadratic program.

A characterization of all stabilizing controllers with delay constraints is provided.

A recursive state-space algorithm for optimal controller design is developed.

Abstract

This paper gives a new solution to the output feedback H2 problem for quadratically invariant communication delay patterns. A characterization of all stabilizing controllers satisfying the delay constraints is given and the decentralized H2 problem is cast as a convex model matching problem. The main result shows that the model matching problem can be reduced to a finite-dimensional quadratic program. A recursive state-space method for computing the optimal controller based on vectorization is given.