Observer design for positive fractional-order interconnected time-delay systems

This paper considers the problem of designing positive reduced-order distributed functional observers for positive fractional-order interconnected time-delay systems. The systems under consideration belong to a class of large-scale fractional-order systems where each system is formed by (Formula presented.) ( (Formula presented.) ) interconnected subsystems with heterogeneous time delays in the interconnections and the local state vectors. First, a necessary and sufficient condition to ensure the positivity of the considered system is derived. Based on this result, (Formula presented.) stand-alone reduced-order positive distributed functional observers for the system are designed. These observers are always nonnegative at any time and they converge asymptotically to the true functional state vectors of the system. The designed observer for each subsystem is based on the local outputs and additional outputs from other subsystems but without the need to exchange the state estimates among the observers. Conditions for the existence of such positive distributed functional observers are derived and they are translated into a linear programming problem. Finally, the effectiveness of the proposed design method is supported by four numerical examples and simulation results.