Non-fragile Consensus Control for Nonlinear Stochastic Multi-Agent Systems with Uniform Quantizations

In this paper, the non-fragile consensus control problem is discussed for a class of discrete time-varying multi-agent systems with stochastic nonlinearities and uniform quantizations. The designed output feedback controller depends on the measurement outputs of a agent itself and its adjacent agents via a given topology, where the uniform quantizations are used to characterize the information transmissions between adjacent agents. The definition of mean-square quasi-consensus is employed to reflect the characteristics of consensus behavior in random case and the controller gain variations are model by the multiplicative noises. We focus on the design of non-fragile output feedback controller such that the consensus performance satisfies the pre-specified upper bound constraint at each sampling instant. By using the linear matrix inequality technique, sufficient conditions are derived to ensure the desired performance requirements and the existence of the controller gain. In addition, the optimal consensus performance is obtained by solving an optimization problem. Finally, a simulation example is utilized to illustrate the usefulness of the proposed non-fragile control method.