PD-type H∞ consensus control for discrete-time stochastic multi-agent systems

The paper is concerned with the H∞ consensus control problem for discrete-time stochastic multi-agent systems with both additive and multiplicative noises. A novel control protocol, namely, PD-type (proportional-derivative-type) control protocol, is proposed to improve the consensus dynamics. By resorting to the well-known Lyapunov stability theory and the matrix inequality techniques, some sufficient conditions are developed to guarantee the considered H∞ consensus. Furthermore, the analytical formula of the controller gains is established with help from the singular value decomposition approach. Finally, the effectiveness of the proposed consensus control scheme is demonstrated through a numerical simulation example.