Design of PI observer for disturbance attenuation and fault detection in linear time-delay systems

The design of Proportional-Integral Observer (PIO) for time-delay systems is considered in this paper. First, a method for PIO design is proposed to attenuate the disturbance to a pre-specified level while estimating the state of the delay system. The method guarantees the stability of the observer and minimizes the H_infin norm between the disturbance and the estimated error. An alternative design procedure, which specifies the allowable size of delay, is also provided. Both designs require solving certain modified algebraic Riccati equations. Due to the fact that attenuation is not the only objective for the designer, a second goal of the paper is to show that PIO has the capability of making simultanous estimation of states and unknown constant disturbance, which can reliably be used in robust fault detection. In this framework, the connections among disturbance observer (DO), unknown input observer (UIO) and PIO are established.