Abstract

In the present paper we obtain a closed form expression for the squared $H_2^{perp}$ norm of a partial fraction expansion with repeated unstable poles. We also obtain a closed form expression for the squared $H_2$ norm of a partial fraction expansion with repeated stable poles. As an application we use the $H_2^{perp}$ result to extend the closed form solution of the discrete-time linear time invariant (LTI) signal-to-noise ratio (SNR) constrained problem to the case of repeated unstable poles in the plant model.