Reduced-Order Observer Design for Time-Delay Systems Using Partial Pole Placement

This paper develops a functional reduced-order observer for a class of Linear Time-Invariant (LTI) systems with time-delay in the state. The proposed observer provides exponentially stable estimation errors. The unbiasedness conditions on the nominal part of the error dynamics of the reduced-order observer were given by employing an algebraic framework. Under such conditions, we propose the use of a partial pole placement of the error dynamical equations to handle sufficient conditions for the existence of the proposed observer. Specifically, we make use of the multiplicity-induced-dominancy property of the characteristic function corresponding to the system's error. The performance and the effectiveness of the developed observer is highlighted through two examples: first, the estimation of the HIV-1 infection dynamics, and second, the improvement of the environmental performance through the study of a diesel engine system.