Proportional integral observer design for linear systems with time delay

A robust proportional integral (PI) observer design for time-delay systems is proposed. It is based on the factorisation approach for time-delay systems. A PI observer in the general form is used. The existence condition for all PI observers is obtained. The parameterisation for all PI observers and their error dynamics for time-delay systems are given. It is indicated that the proposed PI observer is composed of an identity PI state observer and a disturbance signal attenuator. A systematic design procedure for a robust PI observer is presented.