Constant feedback H2 control of systems with statistical uncertainty

The problem of average H₂ control by static (output) feedback is discussed. An uncertain system is controlled, where the system uncertainty is reflected by a probability density function over a set of candidate systems. Necessary conditions for optimality are derived in terms of a feedback and coupled Lyapunov equations. In an example we solve the average performance control problem and compare the resulting average performance controller to worst case types of controllers. Furthermore, in the example we illustrate the dependence of the controller on the probability density