Event-triggered synchronization strategy for complex dynamical networks with the Markovian switching topologies

Area of Science:

• Control Theory
• Network Science
• Systems Engineering

Background:

• Complex networks often face challenges with random switching topologies, impacting system performance and stability.
• Existing synchronization strategies can be communication-intensive, leading to inefficient resource utilization.

Purpose of the Study:

• To propose a novel event-triggered synchronization strategy for complex networks with Markovian switching topologies.
• To reduce communication load and conserve network resources through an optimized triggering mechanism.

Main Methods:

• Modeling network topology switching as a Markov process.
• Developing an event-triggered synchronization strategy that activates only at topology switching instants.
• Converting the synchronization problem into the stability analysis of Markovian jump systems with time-varying delays.
• Utilizing Lyapunov-Krasovskii functionals and weak infinitesimal operations.

Main Results:

• A sufficient condition for the mean square synchronization of complex networks with Markovian switching topologies is established.
• The proposed strategy significantly decreases communication frequency compared to traditional methods.
• Theoretical results are validated through a numerical simulation example.

Conclusions:

• The novel event-triggered strategy effectively achieves mean square synchronization in complex networks with random switching topologies.
• This approach offers a resource-efficient solution for network synchronization problems.
• The findings contribute to the advancement of control theory for complex dynamical systems.