Consensus Problems Of Second-Order Networks With Time-Delays

The multi-agent systems have received much attention recently because of their wide application, such as unmanned aerial vehicles, queue control, etc. For a multi-agent coordination and control system, the most important thing is to design a reasonable protocol or algorithm under which the agents will reach the same state with the evolution of the time i.e., the network can achieve consensus. In practice, the consensus state may be the position, or the velocity.The consensus problem has been a long history. It has been widely sucking in the field of information science, e.g., the automatic theory and the field of distributed computing, it has already been applied. The consensus protocols can be divided into three main categories. They are quantized consensus protocol, discrete-time consensus protocol and continuous-time consensus protocol. The quantized consensus protocol is mainly applied for load balancing. Very little literature concerns about the discrete-time consensus problem. For the continuous-time consensus protocol, it can be divided into first-order, second-order and high-order consensus protocol according to different models. So far, the first-order consensus problem has gotten well studied. For second-order consensus protocols, no researchers consider the network affected by time-delays and switching topologies which should be valuable to address. It is also the main task of this thesis.Our studies suggest that when a network is affected by time-delays and switching topologies, it can still achieve consensus as far as certain conditions are satisfied. Furthermore, using Nyquist theorem, the common upper bound of the time-delay can be calculated. The common upper bound time-delay is dependent on the parameters of the network, so it can reduce the conservatism.