Robust finite-horizon H₂ control

The problem of bounded-variance regulation of an uncertain, linear, continuous-time system, with an unknown norm-bounded parameter matrix, is considered. An upper-bound on the expected value of a quadratic performance index is found for all admissible systems, and regulators are derived that minimize this bound. The resulting regulators consist of a state-feedback gain, and a state-observer. It is found that the design of the feedback gain and the design of the state-observer are separated problems. The design of the observer must account for the fact that the system's uncertainty precludes a precise computation of effect of the known control signal. The tracking problem is also treated, where the output of the controlled system should follow a reference signal that is given in advance.