H ∞ State-Feedback Control of Multi-Agent Systems with Data Packet Dropout in the Communication Channels: A Markovian Approach

The paper presents an H∞ type control procedure for multi-agent systems taking into account possible data dropout in the communication network. The data dropout is modelled using a standard homogeneous Markov chain leading to an H∞ type control problem for stochastic multi-agent systems with Markovian jumps. The considered H∞ type criterion includes, besides the components corresponding to the attenuation condition of exogenous disturbance inputs, quadratic terms aiming to acquire the consensus between the agents. It is shown that in the case of identical agents, a state-feedback controller with Markov parameters may be determined solving two specific systems of Riccati equations whose dimension does not depend on the number of agents. Iterative procedures to solve such systems are also presented together with an illustrative numerical example.