A new method for designing distributed reduced-order functional observers of interconnected time-delay systems

© 2018 The Franklin Institute This paper reports a new method for designing distributed reduced-order functional observers of a class of interconnected systems with time delays. The systems under consideration belong to a class of large-scale systems where each system is formed by a number of interconnected subsystems. Moreover, the interconnections and the states of the local subsystems are subject to heterogeneous time delays. The novel contribution of this paper lies in the development of new coordinate state transformations, which are used to transform the interconnected subsystems into decoupled subsystems. Most significantly, each decoupled subsystem does not contain any time delay in the state vector. Moreover, each decoupled subsystem is expressed in an observable canonical form, with time delays only appearing in the inputs and outputs of the system. Due to this novel structure, a reduced-order functional observer for each decoupled subsystem can be easily designed to estimate the unmeasurable local state vector. The designed observers for the local subsystems do not need to exchange the state estimates amongst themselves, and therefore, each observer for each local subsystem can be designed independently. Because of the state transformations, the designed observers have a more general structure than any of the existing distributed functional observers available in the literature. Numerical examples are given to illustrate the effectiveness and advantages of our results.