Finite-Horizon ${\mathcal H}_{\infty }$ Consensus Control of Time-Varying Multiagent Systems With Stochastic Communication Protocol

This paper is concerned with the distributed <inline-formula> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> consensus control problem for a discrete time-varying multiagent system with the stochastic communication protocol (SCP). A directed graph is used to characterize the communication topology of the multiagent network. The data transmission between each agent and the neighboring ones is implemented via a constrained communication channel where only one neighboring agent is allowed to transmit data at each time instant. The SCP is applied to schedule the signal transmission of the multiagent system. A sequence of random variables is utilized to capture the scheduling behavior of the SCP. By using the <italic>mapping technology</italic> combined with the <italic>Hadamard product</italic>, the closed-loop multiagent system is modeled as a time-varying system with a <italic>stochastic parameter matrix</italic>. The purpose of the addressed problem is to design a cooperative controller for each agent such that, for all probabilistic scheduling behaviors, the <inline-formula> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> consensus performance is achieved over a given finite horizon for the closed-loop multiagent system. A necessary and sufficient condition is derived to ensure the <inline-formula> <tex-math notation="LaTeX">$ {\mathcal {H}}_{ \infty }$ </tex-math></inline-formula> consensus performance based on the completing squares approach and the stochastic analysis technique. Then, the controller parameters are obtained by solving two coupled backward recursive Riccati difference equations. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design scheme.