Optimal Distributed H-infinity State Feedback for Systems with Symmetric and Hurwitz State Matrix

TL;DR

This paper derives a simple, scalable, and distributed optimal H-infinity state feedback control law for LTI systems with symmetric, Hurwitz state matrices, demonstrating its effectiveness through numerical examples.

Contribution

It provides a transparent, easy-to-synthesize optimal control law for systems with symmetric Hurwitz matrices, including distributed and coordinated versions.

Findings

Control law expressed directly in system matrices

Distributed control law applicable to sparse systems

Performance matches Riccati-based optimal controllers

Abstract

We address H-infinity structured static state feedback and give a simple form for an optimal control law applicable to linear time invariant systems with symmetric and Hurwitz state matrix. More specifically, the control law as well as the minimal value of the norm can be expressed in the matrices of the system's state space representation, given separate cost on state and control input. Thus, the control law is transparent, easy to synthesize and scalable. Furthermore, if the plant possess a compatible sparsity pattern it is also distributed. Examples of such sparsity patterns are included. Furthermore, we give an extension of the optimal control law that incorporate coordination among subsystems. We demonstrate by a numerical example that the derived optimal controller is equal in performance to an optimal controller derived by the riccati equation approach.