Reduced order solutions for the singular H∞ filtering problem

In this paper we consider the finite horizon filtering H∞ problem for linear time varying systems. This problem has already been 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, i.e. the matrix F is not full row rank. We will show that in this case a reduced observer can be designed in order to meet the desired performance.