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

Abstract

AbstractThis 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 ‐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.