Distributed H∞ Robust Control of Multiagent Systems With Uncertain Parameters: Performance-Region-Based Approach

Abstract

This article deals with the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> robust control problem for linear multiagent systems perturbed by external disturbances and norm-bounded uncertain parameters over the Markovian randomly switching communication topologies. To tackle this problem, the distributed observer-based controller is proposed, which requires the relative information between neighbors and the absolute information of a subset of the nodes, and thus is intrinsically distributed. It is of great interest to see that the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> robust control problem governed by such a controller can be converted to the stabilization with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> disturbance attenuation problems of some decoupled linear systems, whose dimensions equal those of a single node. Then, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> stochastic robust performance region is defined to indicate the robustness of this controller against the variation of communication topologies. It is theoretically shown that the distributed observer-based controller yields bounded and connected robust performance region. Finally, the theoretical results are verified by conducting numerical simulations and experiments.