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.

Consensus, as the key to coordination of multiagent systems (MASs), has been investigated extensively in recent years [

In fact, studies on structurally unbalanced signed digraph have already been reported in [

With these observations, in this work, we investigate sign-consensus for LTI MASs under signed digraphs. The agents’ states are reconstructed, and state observer-type protocols based on them are given. By using tools from matrix analysis and ordinary differential equation theory, the closed-loop system is analyzed. It is shown that if the graph adjacency matrix has strong Perron–Frobenius property or is eventually positive, sign-consensus for LTI MASs can be achieved. Our main contributions are as follows. First, the agent dynamics are extended to be LTI system, not limited to integrators [

The state observer-type consensus protocol is proposed in Section

For a matrix or vector

Assume

For

Consider an MAS with

The communication topology among agents is represented by a signed digraph

The system in (

From Definition 1, given any initial value, the states of agents in (

Let

where

Since

Next, we will demonstrate that the system in (

Suppose that

Define

Since

By assumption,

Obviously,

Since

In Theorem 1, sign-consensus is achieved based on a state observer-type protocol. This is different from protocols in [

For the system in (

By assumption,

From (

For the system in (

In Corollary 1, if the requirement on

Consider the system in (

Obviously,

Note that

Communication topology among 6 agents.

State trajectories of

State trajectories of

State estimate error trajectories of

State estimate error trajectories of

The sign-consensus of MASs is investigated where each agent is described by an LTI system. A state observer-type protocol is designed, which is more practical than the usual state feedback protocols. It is shown that if the adjacency matrix has strong Perron–Frobenius property or is eventually positive, then sign-consensus can be achieved based on the proposed protocols.

The MATLAB code used in the example can be obtained from the corresponding author.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (grant no. 61973183), Natural Science Foundation of Shandong Province (grant no. ZR2019MF041), and the Youth Creative Team Sci-Tech Program of Shandong Universities (grant no. 2019KJI007).