Matrix-weighted consensus of fractional-order networked systems via sampled-data control

Area of Science:

• Control Systems Engineering
• Networked Systems Theory
• Fractional Calculus Applications

Background:

• Fractional-order systems exhibit complex dynamics influenced by memory effects.
• Networked systems require robust control strategies for distributed decision-making.
• Matrix-weighted coupling introduces sophisticated interaction patterns among agents.

Purpose of the Study:

• To investigate consensus achievement in fractional-order networked systems with matrix-weighted coupling.
• To design a distributed sample-based control strategy for state synchronization.
• To derive necessary and sufficient conditions for consensus in various network topologies.

Main Methods:

• Development of a distributed control strategy utilizing sampled data for agent state updates.
• Analysis of matrix-weighted Laplacian properties, including eigenvalue distribution.
• Derivation of consensus conditions based on sampling period, fractional order, control gains, and network structure.

Main Results:

• Established consensus conditions for both undirected and directed matrix-weighted networks.
• Demonstrated that consensus in undirected networks is linked to the null space of the matrix-weighted Laplacian.
• Proved that a positive spanning tree is not required for achieving consensus in directed networks.

Conclusions:

• The proposed sample-based control strategy effectively achieves consensus in fractional-order systems with matrix-weighted coupling.
• The derived conditions provide critical insights into the influence of network topology and system parameters on consensus.
• Simulation results validate the theoretical findings, confirming the strategy's practical applicability.