Estimation of perturbation bounds for finite trajectories

The problem of estimating perturbation bounds for finite trajectories of non-autonomous systems is considered. A worst case sensitivity derivative of the trajectory with respect to the uncertainty is used to verify that the perturbed trajectory is within a given neighborhood of the nominal. This gives rise to a robust control problem for linear time-varying systems. It is shown that relaxation using integral quadratic constraints and the solution to a linear quadratic optimal control problem can be used to find bounds on the robust control problem.