Observer-based distributed control of large-scale systems under gossip communication protocol

This note is concerned with the observer-based distributed control problem of large-scale systems under gossip communication protocol. Random binary variables that satisfy a certain conditional probability distribution are introduced to model gossip communication protocol. In such a protocol, each subcontroller receives information from only one randomly chosen neighbor at each instant. Novel observer-based distributed controllers are proposed for large-scale systems. Based on Lyapunov stability theory and stochastic matrix manipulations, sufficient conditions are established such that the closed-loop system is exponentially mean square stable and the prescribed L2-gain performance is satisfied. Then these conditions are transformed into linear matrix inequalities. The observer gains and controller gains can be obtained by solving a set of linear matrix inequalities. Finally, two numerical examples are used to illustrate the effectiveness of the proposed theoretical results.