Stabilization with unknown-input estimation for time-delayed systems using functional-observer-based feedback control design

This paper focuses on the stabilization and unknown-input estimation (UIE) problem of continuous-time delayed systems by virtue of functional-observer (FO)-based feedback controller. It allows us to estimate the unknown external variable that degrades the system performance with respect to the partially known input of the system. In particular, the unknown inputs are considered in system dynamics's state as well as in output, which makes the addressed problem to be more applicable. In addition to that, the aim is then to design minimal order functional observer. Notably, the FO-based feedback control law is introduced for the first time and it is used to ensure the asymptotic stabilization with UIE of the proposed system. Whilst, the design and analysis of UIE and FO is based on Lyapunov stability theory and applying the inequality analysis technique, the sufficient stability conditions are established in the forms of matrix inequality. Eventually, the numerical examples with simulation results are provided to validate the practicability and efficacy of the developed control strategy.