A New Characteristic of Switching Topology and Synchronization of Linear Multi-Agent Systems

The concept of synchronizability exponent is proposed to define a quantitative characteristic of switching topology. Meanwhile, the Lyapunov exponent is introduced as a quantitative characteristic of agent dynamics. A quantitative relation that the Lyapunov exponent is less than the synchronizability exponent is presented as a new synchronization condition. This condition describes the relationship between agent dynamics and switching topology, which does not seem to have been explicitly considered so far. Under the new quantitative condition, we design state feedback and output feedback protocols to achieve synchronization of linear multiagent systems. We further show that the output feedback protocols can be constructed by separately designing state feedback protocols and state observers, namely the separation principle holds.