Containment Control And Frequency Domain Criteria Of General Linear Multi-agent Systems With Time Delay

Containment control problems for general linear multi-agent systems with time delay are studied under the directed network topology. A distributed protocol with time-varying delays is proposed. With the method of Lyapunov function, a sufficient condition, which is related to the upper bound of the range of delay and the derivative of time-varying delay, is given to ensure containment control. Moreover, when delay is time-invariant, a sufficient condition, which is related to the time-delay, is given to en-sure containment control. When time-delay is an unknown constant, an upper bound of delay is also obtained by using frequency-domain analysis method, which depends on agent dynamics and network topology. Finally, a simulation is given to demonstrate the effectiveness of the obtained theoretical results.