Asymptotic regulation with H2 disturbance rejection

The problem of optimal H₂ rejection of stochastic disturbances while achieving asymptotic tracking of uncertain commands and asymptotic rejection of uncertain deterministic disturbances is considered. The internal model principle is used to ensure that the expected value of the tracking error approaches zero asymptotically. Necessary conditions are given to characterize controllers that minimize a performance measure consisting of an H₂ disturbance rejection cost plus an upper bound on the integral square error cost for transient performance. The necessary conditions provide expressions for gradients of the cost with respect to each of the which can be utilized via numerical methods to determine optimal control gains