Transfer functions of closed-loop systems in H2 optimal control

This paper is concerned with explicit descriptions of the optimal closed-loop system for H₂ control problems in the case of single-input and single-output linear systems. We focus on two typical H₂ optimal control problems, the minimal energy problem and optimal tracking control problem, and show that the transfer functions of the optimal closed-loop systems can be described in specific terms of the denominator and numerator polynomials of the plants. Moreover, we derive the positions or the area of poles and zeros of the closed-loop system.