Variance constrained H₂/H_∞ control

In this paper dual problems, which we shall call output and input variance constrained H₂/H_∞ controls, are considered. In these problems, we seek control-laws that minimize an H₂ performance criterion subject to an H_∞ performance bound as well as multiple variance constraints on either outputs or inputs of time-invariant multivariable systems. Based on the investigation of Kuhn Tucker optimality conditions to the equivalent optimization problems, first order necessary conditions are obtained for a regular point that minimizes an upper bound on quadratic performance subject to H_∞-norm and variance inequality constraints. Second-order necessary and sufficient conditions for the optimization problems are investigated and efficient algorithms for synthesizing the controllers are proposed.