An algorithm for mixed H ₂ /H _∞ robust controllers that satisfy variance constraints

In this paper an iterative procedure is developed for synthesizing mixed H ₂ /H _∞ robust controllers that satisfy output variance constraints. In this synthesis problem, we seek control-laws for linear systems that minimize an upperbound on a quadratic performance subject to both H _∞ -norm and output variance constraints under the presence of structured uncertainties. The approach taken in this paper is to convert the problem into an equivalent nonlinear programming with both equality and inequality constraints. Kuhn Tucker optimality condition is employed in order to obtain first order necessary condition for a regular point that minimizes an upperbound 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. Dual problem that imposes constraints on input variance, is also discussed.