Robust State Observer Design for Dynamic Connection Relationships in Complex Dynamical Networks

The complex dynamical network with the time-varying links may be regarded to be composed of the two mutually coupled subsystems, which are called the nodes subsystem and the connection relationships subsystem respectively. Designing the state observer for the nodes subsystem has been discussed in some existing researches by employing the known connection relationships. However, the state observer design for the connection relationships subsystem is not shown in the existing researches. In practical applications, the connection relationships subsystem possesses also the state variables such as the relationship strength in social network, the size of web tension in the web winding system. Therefore, designing the state observer for the connection relationships subsystem is also of practical significance. In this paper, a novel state observer is proposed for the connection relationships subsystem modeled mathematically by the Riccati matrix differential equation. The observer utilizes the output measurements of the connection relationships subsystem and the state of nodes subsystem. Compared with the state observer of nodes subsystems which employs the known connection relationships, the state observer for the connection relationships subsystem employs the state of nodes subsystem and is represented in form of the matrix differential equation. By using Lyapunov stability theory, it is proved in this paper that the state observer for the connection relationships subsystem is asymptotical under certain mathematic conditions. Finally, the illustrative simulation is given to show the efficiency and validity of the proposed method in this paper.