An algorithm for mixed H2/H∞ robust controllers that satisfy variance constraints

An iterative procedure is developed for synthesizing mixed H ₂/H_∞ robust controllers that satisfy output variance constraints. In this synthesis problem, the authors seek control laws for linear systems that minimize an upper bound on a quadratic performance subject to both H_∞ -norm and output variance constraints in the presence of structured uncertainties. The approach taken is to convert the problem into an equivalent nonlinear programming problem with both equality and inequality constraints. The Kuhn-Tucker optimality condition is used to obtain a first-order necessary condition for a regular point that minimizes an upper bound on quadratic performance for the given H _∞-norm and variance constraints. Based on this condition, an iterative algorithm for synthesizing the controllers is developed. To demonstrate the effectiveness of the algorithm, an illustrative example is presented. A dual problem that imposes constraints on input variance is also discussed