<inline-formula> <tex-math notation="TeX">$H_{\infty}$</tex-math></inline-formula> Consensus Achievement of Multi-Agent Systems With Directed and Switching Topology Networks

Abstract

The consensus problems with $H_{\infty}$ and weighted $H_{\infty}$ bounds for a homogeneous team of linear time-invariant (LTI) multi-agent systems with a switching topology and directed communication network graph are studied in this technical note. Sufficient conditions to design distributed controllers are proposed based on state feedback corresponding to bounded $L_{2}$ gain and rms bounded disturbances. Based on the solution of an algebraic Riccati equation that circumvents the need to solve linear matrix inequalities (LMIs), a design methodology is proposed to properly select the controller gains. The stability properties of the proposed controllers are then investigated based on Lyapunov analysis. The effectiveness of our proposed consensus algorithms are then illustrated by performing simulations for diving consensus of a team of unmanned underwater vehicles (UUVs).