H∞H∞ consensus control for multi-agent systems with missing measurements: The finite-horizon case

This paper deals with the H∞H∞ consensus control problem for a class of discrete time-varying multi-agent systems with both missing measurements and parameter uncertainties. A directed graph is used to represent the communication topology of the multi-agent network, and a binary switching sequence satisfying a conditional probability distribution is employed to describe the missing measurements. The purpose of the addressed problem is to design a time-varying controller such that, for all probabilistic missing observations and admissible parameter uncertainties, the H∞H∞ consensus performance is guaranteed over a given finite horizon for the closed-loop networked multi-agent systems. According to the given topology, the measurement output available for the controller is not only from the individual agent but also from its neighboring agents. By using the completing squares method and stochastic analysis techniques, necessary and sufficient   conditions are derived for the H∞H∞ consensus to be ensured, and then the time-varying controller parameters are designed by solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the usefulness of the proposed control protocol.