H∞H∞ consensus performance for discrete-time multi-agent systems with communication delay and multiple disturbances

This paper proposes a new H∞H∞ consensus criterion for discrete-time multi-agent systems with communication-delay and disturbances. By constructing a suitable Lyapunov–Krasovskii (L–K) functional, which fractionizes the delay interval into two subsections, and utilizing reciprocally convex approach, a new H∞H∞ consensus criterion for the concerned systems is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. One numerical example is given to illustrate the effectiveness of the proposed method.