Mixed H₂/H_∞ control under variance constraints

Dual problems, which we call output and input variance constrained H₂/H_∞ controls, are considered. In these problems, we seek control-laws that satisfy mixed H₂/H_∞ performance criteria, under multiple variance constraints on either outputs or inputs of time-invariant multivariable systems. The approach taken is to convert the problems into non-linear programming with both equality and inequality constraints. For both problems, the Kuhn-Tucker optimality condition is employed to obtain a first-order necessary condition for a regular point that minimizes an upper bound on the quadratic performance for the given H_∞ constraint. A second-order necessary condition and sufficiency for the strict local minimizer of the upper bound are investigated. Efficient algorithms for synthesizing the desired controllers are proposed.