Consensus under communication delays

• Main Authors: Seuret, Alexandre, Dimarogonas, Dimos V., Johansson, Karl Henrik
• Format: Others
• Language: English
• Published: KTH, Reglerteknik 2008
• Subjects: Analytic expressions; Communication delays; Communication networks; Consensus problems; Constant delays; Frequency approaches; Infinite dimensional; Initial conditions; Lyapunov-Krasovskii; Network communication schemes; State informations; Time- delays; Time-delay systems; Communication; Delay control systems; Linear control systems; Telecommunication networks; Time delay; Stability criteria; Systems engineering; Systemteknik
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-28520

This paper deals with the consensus problem under communication network inducing delays. It is well-known that introducing a delay leads in general to a reduction of the performance or to instability due to the fact that timedelay systems are infinite dimensional. For instance, the set of initial conditions of a time-delay system is not a vector but a function taken in an interval. Therefore, investigating the effect of time-delays in the consensus problem is an important issue. In the present paper, we assume that each agent receives instantaneously its own state information but receives the state information from its neighbors after a constant delay. Two stability criteria are provided based on the frequency approach and on Lyapunov-Krasovskii techniques given in terms of LMI. An analytic expression of the consensus equilibrium which depends on the delay and on the initial conditions taken in an interval is derived. The efficiency of the method is tested for different network communication schemes. === <p>QC 20110120</p>