Minimum energy controllers with inequality constraints on output variances

We consider the design of control systems to minimize the input energy subject to output variance inequality constraints. Necessary and sufficient conditions are developed for state feedback, measurement feedback and dynamic controllers. We find that all these problems are equivalent to LQ problems with a diagonal output weighting matrix Q , where Q has some interesting properties which reflect the importance of each constraint. An algorithm which iteratively selects the weight Q is given. Similar results are also derived for the dual problem where input variance inequality constraints are desired. All these results can be applied to the deterministic case with inequality constraints on the L ∞ ,‐norm of the outputs.