Repeated Poles in Feedback over a Class of Signal-to-Noise Ratio Constrained Channels

Abstract

In the present paper we obtain a closed form expression for the squared H ⊥ 2 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 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.