Consensusability Margin Optimization for Second-Order Multiagent Systems With Communication Uncertainties

Abstract

In this article, 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> optimization approach is used to study the consensusability margin optimization problems for distributed second-order sampled-data multiagent systems with communication uncertainties. The considered uncertainties are frequency-dependent and bounded in <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> norms. Specifically, for both the state-based protocols with relative damping and absolute damping, this article attempts to answer two questions: 1) how to characterize the control parameters for achieving robust consensus; and 2) what is the maximal consensusability margin and how to find, if one exists, the parameter to achieve this optimal performance. It is shown that the consensusability margin optimization problems are constraint optimization problems, which are to be specified by specific problem parameters and can be discussed by designing the network complementary sensitivity function matrices of the closed-loop multiagent systems. Moreover, it is shown that the infimums of 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> norms of the network complementary sensitivity function matrices under both protocols are independent of network topologies.