A probabilistic approach to robust control design

A probabilistic approach to the disturbance attenuation problem for LTI discrete-time systems is proposed. The performance is measured by a probability with respect to the stochastic noise of which the worst case 2-norm of the output against a class of deterministic signals with bounded 2-norm is less than a specified level. We first provides a matrix inequality characterization of the probability based on the Toeplitz form of the system and derive a lower bound of the probability. We then show that a guaranteed performance level can be computed by solving an LMI convex optimization problem.