Sign‐Consensus of Linear Multiagent Systems under a State Observer Protocol

Abstract

The sign-consensus problem for linear time-invariant systems under signed digraph is considered. The information of the agents’ states is reconstructed, and then, a state observer-type sign-consensus protocol is proposed, whose performance is analyzed using matrix analysis and ordinary differential equation theory. Sufficient conditions for ensuring sign-consensus are given. It is proven that if the adjacency matrix of the signed digraph has strong Perron–Frobenius property or is eventually positive, sign-consensus can be achieved under the proposed protocol. In particular, conventional consensus is a special case of sign-consensus under mild conditions.

Upper bounds for the spectral radius of matrices having the Perron–Frobenius property

“…Bounds (1), ( 2), (3), and (4) for ρ(M -1 N) are given in Table 2. From Table 2 it can be seen that bounds (1), (2), and (3) are larger than 1. However our bound (4) is less than 1, which implies that we can conclude that the Perron-Frobenius splitting for this case is convergent by our bound.…”

“…Matrices having the Perron-Frobenius property [7] arise in many different fields of science and engineering, such as steady state behavior of Markov chains, population growth models, and Web search engines [2,9,11,12].…”

Adaptive fully-distributed sign-consensus control approach for nonlinear multi-agent systems over a signed graph

“…In contrast, the sign-consensus problem deals with attainment of same sign of states of agents with different magnitudes. Some recent studies have explored the sign-consensus problems in Jiang and Zhang (2016); Jiang et al (2016a); Jiang et al (2016b); Jiang et al (2017a); Jiang et al (2017b); Jiang et al, (2018); Diao and Ma (2019); Wang et al (2020); however, these results are limited to linear systems. To the best of our knowledge, the problem of the sign-consensus for the Lipschitz nonlinear multi-agents has not been addressed in the existing research works.…”