Expected H2 performance control for systems with statistical uncertainty

This paper deals with the problem of controlling an uncertain linear time invariant dynamical system, where it is assumed that there exists a certain probability distribution over the uncertainty. The performance measure is the square of the H₂ norm of the closed loop transfer function and we focus on the expected performance. It is shown that the expected performance is a well defined and smooth function of both the uncertainty parameters and controller parameters. Furthermore, it is shown that the locally optimal expected performance controller is a unique and smooth function of the probability distribution