On the Design of Structured Stabilizers for LTI Systems

TL;DR

This paper introduces a new, efficient method for designing structured static state-feedback controllers for LTI systems, relaxing previous conservativeness and applicable to various control scenarios.

Contribution

It presents a novel solution leveraging the Projection Lemma for structured stabilizer design, improving computational efficiency and reducing conservativeness over existing methods.

Findings

The proposed approach is computationally efficient.

It is less conservative than previous methods.

Numerical examples demonstrate its effectiveness.

Abstract

Designing a static state-feedback controller subject to structural constraint achieving asymptotic stability is a relevant problem with many applications, including network decentralized control, coordinated control, and sparse feedback design. Leveraging on the Projection Lemma, this work presents a new solution to a class of state-feedback control problems, in which the controller is constrained to belong to a given linear space. We show through extensive discussion and numerical examples that our approach leads to several advantages with respect to existing methods: first, it is computationally efficient; second, it is less conservative than previous methods, since it relaxes the requirement of restricting the Lyapunov matrix to a block-diagonal form.