A low-order linear functional observer for time delay systems

This paper presents an efficient technique to design low-order state function observers for linear time-delay systems. Assuming the existence of a linear state feedback controller to achieve stability or some control performance criteria of the time-delay system, a design procedure is proposed for reconstruction of the state feedback control action. The procedure involves solving an optimisation problem with the objective to generate a matrix that is as close as possible to the given feedback gain of the required feedback controller. A condition for robust stability of the time-delay system using the observer-based control scheme is given. The attractive features of the proposed design procedure are that the resulted linear functional state observer is of a very low order and it requires information of a small number of outputs. Numerical examples are given to demonstrate the design procedure and its merits.