Stochastic bounded consensus for multi-agent systems with fractional Brownian motions via sliding mode control

Utilizing the sliding mode control method, the analysis of the finite-time stochastic bounded consensus for multi-agent systems under the disturbance of fractional Brownian motions with semi-Markovian jumping topologies is investigated. Semi-Markov jumping topologies are introduced to describe the information interaction between agents. In order to obtain the sliding mode error dynamics between leader and followers, an integral sliding mode surface based on neighbor information of agents is designed considering semi-Markovian jumping topologies. Different from the normal Lyapunov functional, a double-integral-type Lyapunov functional based on the Hurst index is constructed to deal with fractional Brownian motions, then the finite-time stochastic bounded consensus of sliding mode dynamics are studied. Then the finite-time reachability of the error system state to the proposed sliding mode surface is analyzed. Last a distributed microgrid model and a numerical example are given and simulated to verify the effectiveness of the proposed method.