Distributed filtering and control for time delay systems interconnected over an undirected graph

Abstract

In this paper, the delay-dependent filtering and delay-independent control problems for time delay systems interconnected over an undirected graph are considered. Sufficient conditions are first developed on the well-posedness, delay-independent/delay-dependent stability and contractiveness for the plant, respectively. Then, the filtering problem, i.e. the problem to design a distributed filter such that the filtering error system is well-posed, delay-dependent stable and contractive, is investigated. A sufficient condition on the existence of such a filter is presented in terms of linear matrix inequalities (LMIs), which provides an effective way to obtain an appropriate filter inheriting the same graph as the plant. For the control problem, since it is still very difficult to establish a method for designing delay-dependent controller, we restrict the problem to the delay-independent case. A sufficient condition is developed for the existence of a distributed output-feedback controller which inherits the structure of the plant and ensure the closed-loop system to be well-posed, delay-independent stable and contractive. An algorithm is also proposed for designing an appropriate controller through numerical solutions of a set of LMIs. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of the proposed design methods.

Keywords:

• Distributed filters
• distributed controllers
• time delay systems
• interconnected over an undirected graph

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of PR China under Grant 61673218 and the Japan Society for the Promotion of Science (JSPS.KAKENHI15K06072).