ℋ∞ Consensus Control of Multi-agent Systems with Round-robin Protocol and Missing Measurements: The Finite-horizon Case

Abstract

The ℋ ∞ consensus control problem is handled for a class of discrete time-varying multi-agent systems with round-robin protocol and missing measurements. The round-robin protocol is considered, which allows only one agent can send its measurement data at each transmission step in order to prevent the data collisions. And the missing measurements phenomenon is described by a sequence of Bernoulli distributed random variables with known probabilities. We focus on designing the controller parameters to guarantee that the closed-loop multi-agent systems with missing measurements satisfy the ℋ ∞ consensus performance. On this basis, some sufficient and necessary conditions are obtained by solving coupled backward recursive Riccati difference equations, where the existence and feasibility of the control scheme can be obtained with the help of the completing squares method and the stochastic analysis technique. At last, a numerical example is given to illustrate the effectiveness of the developed controller design scheme.