A distributed state observer scheme for interconnected discrete time-delay systems

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