Observer design for Multi-Rate Linear Systems with Delayed Output

In this article, a “Backward in Time Observer” has been designed for linear systems having time delays in output measurements and differences in the sampling rate of input and output measurements. With the proposed observer we are able to recover the performance of the system with no time delay and an equal sampling rate of input and output measurements. Different observers have been designed for time delayed systems by the researcher, but multi-rate time delayed systems have not been discussed so far, hence our proposed observer is able to cater for both of these problems in the system. The proposed observer is simulated for the seeker system of the missile for verification and illustration. Seeker system of missile is a linear time-invariant system having time delay in output measurement. Furthermore, the output measurement through IR camera of the seeker system has a lower sampling rate than its input signal from the gyro.