Robust consensus for linear multi-agent systems with structured uncertainties

ABSTRACT

This paper addresses a robust ${\mathcal{H}}_{\mathrm{\infty }}$ consensus problem for linear multi-agent systems subject to structured uncertainty and external disturbances under the leaderless framework. A distributed dynamic output-feedback protocol is proposed, which utilises not only relative output information of neighbouring agents but also relative state information of neighbouring controllers. Through model transformations, the robust ${\mathcal{H}}_{\mathrm{\infty }}$ consensus control problem of multi-agents network is reduced to a set of independent ${\mathcal{H}}_{\mathrm{\infty }}$ stabilisation problems for single linear subsystems. For robust ${\mathcal{H}}_{\mathrm{\infty }}$ consensus, it is shown that the analysis and full state-feedback synthesis conditions for such subsystems can be formulated as linear matrix inequality (LMI) optimisation problems. On the other hand, the synthesis condition for dynamic output-feedback protocol is formulated as non-convex bilinear matrix inequality (BMI) optimisation problem. An iterative LMI algorithm is then presented to solve the resulting BMI optimisation problem. An example of multiple mass-spring-damper systems has been used to demonstrate theoretical results.

KEYWORDS:

• Uncertain linear multi-agent systems
• structured uncertainty
• distributed control
• output-feedback protocol
• bilinear matrix inequality

Disclosure statement

No potential conflict of interest was reported by the authors.