Reduced-order solutions for the singular H/sup /spl infin// filtering problem

We consider the filtering H/sup /spl infin// problem for linear time-varying systems. This problem has been already solved in the case when the direct feedthrough matrix F between the disturbance and the output vectors is full-row rank. Here, we consider the case when the problem is singular, that is when this feedthrough matrix is not full-row rank. We show that in this case a reduced-order observer can be designed to meet the desired performance. Moreover, we apply the obtained results to solve a particular H/sup /spl infin// singular output feedback problem.