Performance Analysis And Distributed Filtering Of Discrete Time-Delay Systems Interconnected Over An Arbitrary Graph

The interconnected system consists of spatially or wirelessly interconnected units or subsystems.The theoretical study of the interconnected system is becoming more and more sophisticated.The interconnected system over an arbitrary graph is also of great research importance in practical engineering,such as automated highway networks,networked information systems,and unmanned aircraft formation flight.Time delay is an inevitable phenomenon in control theory and engineering,and there will also be time delays in interconnected systems.This paper focuses on the stability and distributed filtering of discrete time-delay systems interconnected over an arbitrary graph.The main contents are as follows.Firstly,we give the definitions of well-posedness,exponential stability and contractiveness for discrete time-delay systems interconnected over an arbitrary graph.A sufficient condition has been developed of the well-posedness,exponential stability and contractiveness is established by constructing a suitable Lyapunov-Krasovskii functional.We use the Jensen inequality to deal with the non-linear terms in the difference equation of the Lyapunov-Krasovskii functional.A numerical example is utilized to verify the obtained results.Secondly,we propose an improved condition of the well-posedness,exponential stability and contractiveness for discrete time-delay systems interconnected over an arbitrary graph.We use the Wirtinger inequality to deal with the non-linear terms in the difference equation of the Lyapunov-Krasovskii functional.A sufficient condition is obtained in the form of linear matrix inequalities.A numerical example is utilized to verify the obtained results.At last,we will design a distributed filer for discrete time-delay systems interconnected over an arbitrary graph.A sufficient condition for the well-posedness,exponential stability and contractiveness of the filtering error system is established.We derive a sufficient condition for the existence of the distributed filter using Finsler’s Lemma.At the same time,we give a method for solving the filter parameters.A numerical example is utilized to verify the obtained results.