H_∞ and H₂ Almost Synchronization of Continuous-Time Linear MAS

So far we considered several synchronization problems for a MAS. Most research has focused on the idealized case where the agents are not affected by external disturbances. In the literature where external disturbances are considered, γ-suboptimal H_∞ design is developed for a MAS to achieve H_∞ norm from an external disturbance to the synchronization error among agents less than to an a priori given γ. In particular, Li et al. (IEEE Trans Circ Syst-I Regular papers 57(1):213–224, 2010), Zhao et al. (Int J Contr 85(3):32–341, 2015) considered the H_∞ norm from an external disturbance to the output error among agents. Saboori and Khorasani (IEEE Trans Aut Contr 59(11): 3104–3109, 2014) considered the H_∞ norm from an external disturbance to the state error among agents. These papers do not present an explicit methodology for designing protocols. The papers Lin and Jia (IET Control Theory Appl 4(3), 487–498, 2010) and Lin et al. (Syst Contr Lett 57(8):643–653, 2008) try to obtain an H_∞ norm from a disturbance to the average of the states in a network of single or double integrators.