Consensus of Multiagent Systems With Time-Varying Delays and Switching Topologies Based on Delay-Product-Type...

Area of Science:

• Control Systems Engineering
• Networked Systems Theory
• Applied Mathematics

Background:

• Consensus in multiagent systems (MASs) is crucial for coordinated behavior.
• Time-varying delays and switching topologies introduce significant challenges to achieving consensus.
• Existing consensus conditions can be overly conservative, limiting practical applications.

Purpose of the Study:

• To develop less conservative consensus conditions for MASs with time-varying delays and switching topologies.
• To determine the maximal allowable upper bound for time-varying delays in such systems.
• To extend the findings to leader-following consensus problems with nonlinear dynamics.

Main Methods:

• Construction of a novel delay-product-type Lyapunov-Krasovskii functional (LKF) using auxiliary function-based integral inequality (AFBII).
• Introduction of the generalized reciprocally convex matrix inequality (GRCMI) and a relaxed quadratic function negative-determination lemma.
• Design of a proportional and derivative-like (PD-like) control protocol.

Main Results:

• Derivation of new, less conservative conditions for achieving consensus in MASs.
• Determination of the maximal allowable upper bound for time-varying delays.
• Successful extension to leader-following consensus problems with Lipschitz nonlinear dynamics.
• Validation through illustrative examples, including Chua's circuit.

Conclusions:

• The proposed methods provide improved and less conservative criteria for MAS consensus.
• The established maximal delay bound enhances the robustness of consensus protocols.
• The study offers effective solutions for complex MAS coordination problems with practical implications.