Convex synthesis for optimal ℋ∞ consensus of input-delayed multi-agent systems via dynamic relative output feedback

Abstract

In this paper, we address the leaderless consensus control problem for a class of linear multi-agent systems (MASs) subject to nonlinear time-varying input delays and unknown external disturbances. The MAS is considered to be non-introspective, meaning that each individual agent is not able to measure the absolute plant state/output of its own but can sense relative information from its neighbours. A novel dynamic relative output-feedback (DROF) controller structure is proposed by leveraging the integral quadratic constraints (IQCs) from robust control theory. This new DROF controller is compelling in the sense that it utilises not only the relative plant outputs, but also the relative controller states and relative IQC-induced dynamics states for distributed feedback control. Based on this, the associated consensus control synthesis conditions that guarantee optimal disturbance attenuation performance in the presence of time-varying input delays are derived and formulated as linear matrix inequalities (LMIs), which can be solved efficiently via convex optimisation. Effectiveness of the proposed theoretical results is demonstrated through simulation studies.