Observer for interconnected discrete time-delay systems

This paper presents an observer for interconnected discrete-time systems with multiple delays in both the state and control vectors. The proposed state observer is composed of two parts. The first consists of a local dynamic part and the second consists of a static part. The dynamic part is constructed using only local information. Its order is equal to the number of unstable and/or poorly damped eigenvalues of the system. The static part is constructed based on the knowledge of the control input to each subsystem. It is shown that local states for each subsystem can be estimated with arbitrarily chosen dynamics. A simple design method is presented. A numerical example is given to illustrate both observer properties and design method.