Event-triggered consensus control and fault estimation for time-delayed multi-agent systems with Markov switching topologies

Abstract

This paper focuses on the consensus control and fault estimation problems for a class of time-delayed multi-agent systems with Markov switching topologies. Two different event-triggered mechanisms are adopted with hope to reduce burden of shared network and improve energy efficiency. Under Markov process, by establishing the consensus control protocol and designing a novel adaptive fault estimation observer, the consensus control and fault estimation problems are transformed into two stochastic stability problems in different forms. Then, according to the switching Lyapunov function method and free-weighting matrix technique, two delay-dependent stability criteria on the consensus control and fault estimation are derived, respectively. However, the two criteria containing nonlinear coupling terms are not standard linear matrix inequalities (LMIs) and cannot be solved directly with the LMI toolbox. In order to eliminate the coupling terms, two improved path-following algorithms are presented. These algorithms depend on the initial conditions, so it is very crucial to choose the appropriate preset parameters. The computational complexity is increasing with the number of iterations, system size and matrix dimension, which is a fully new challenge for the study of consensus control and fault estimation of multi-agent systems. Based on the algorithms, the switching consensus controller gains and model gain matrices of fault estimation can be efficiently solved out. Finally, a simulation example of tailless fighter airplanes is given to illustrate the practicality and validity of the theoretical results.