H ∞ control for a class of multi‐agent systems via a stochastic sampled‐data method

Abstract

In this study, the stochastic sampled-data approach is developed to deal with the H ∞ control problem for a class of linear multi-agent systems. For each agent, signals should be transmitted to the control input, including not only its own measurements, but also the output information received from the neighbour agents. The relationships of information communications between the whole multi-agents are totally reflected by a weighted directed graph with a fixed topology structure. To the addressed problem, the author's focus is to design an output feedback controller for each agent such that, for the external energy bounded disturbances, the exponential stability in the mean square sense and interference rejection ability under consideration can be guaranteed. By assuming that the sampling period of each agent switches between two values in a probabilistic way, the stochastic sampling phenomenon is well characterised in every sampling tasks. In virtue of Lyapunov theory and semi-definite programming method, sufficient conditions are derived to ensure the exponential stability as well as H ∞ performance, and the feedback controllers are also designed by solving some certain matrix inequalities. Finally, a numerical simulation is given to demonstrate the validness of the proposed control strategy.