Bipartite consensus for second-order multi-agent systems with external disturbances via constraint data-sampled impulsive method

This paper is aimed to deal with bipartite consensus for nonlinear second-order multi-agent systems (MASs) with external disturbances. Due to the existence of nonlinearity and external disturbances (containing bounded disturbances and stochastic disturbances separately), the original MASs are not stable. In this paper, the impulse signal at each impulsive instant only happens between the leader and followers. In order to consume less energy in the limited operating range of actuator, the input saturation function is taken into consideration to implement data-sampled control with impulsive information. Constraint data-sampled method and leader-following impulsive protocol are combined together under signed topology to deal with the extended bipartite consensus. Results show that some sufficient conditions relying on impulsive gains and convex combination parameters can be derived to reach the goal. Two numerical examples of simple pendulums illustrate the availability of theoretical analyses.