On the design of robust controllers for arbitrary uncertainty structures

The focal point of this paper is the design of robust controllers for linear time-invariant uncertain systems. Given bounds on performance (defined by a convex performance evaluator) the algorithm converges to a controller that robustly satisfies the specifications. The procedure introduced has its basis on stochastic gradient algorithms and it is proven that the probability of performance violation tends to zero asymptotically faster than 1/k, where k is the iteration step. Moreover, this algorithm can be applied to any uncertain plant, independently of the uncertainty structure. As an example of application of this new approach, we demonstrate its usefulness in the design of robust H₂ controllers.