State space approach to control design under partial statistical information for exogenous signals

We consider a class of control design problems for discrete linear time invariant systems where the statistical information available on the exogenous signals is incomplete. The control objective is to minimize the worst case variance of the regulated output over the class of all exogenous signals that meet the available prior statistical information. State space necessary and sufficient conditions for analysis and control design are presented using linear matrix inequalities (LMI) and bilinear matrix inequalities. These results, which provide a state space treatment of some of the results presented by Gusev (1994, 1995), can also be viewed from a theoretical perspective as a bridge between the H₂ and H_∞ design methodologies. For clarity of exposition and a more transparent signal theoretic interpretation, only the single input single output case is treated