@MISC{Jonsson00estimationof, author = {Ulf T. Jonsson}, title = {Estimation of Perturbation Bounds for Finite Trajectories}, year = {2000} }

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Abstract

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. 1Introduction The following robustness problem for finite time trajectories of non-autonomous systems is considered: Find conditions which ensure the existence of a unique solution within a given neighborhood of the nominal solution when the system is perturbed with a class of structured uncertainties. We consider time-varying parametric uncertainty and dynamic uncertainty. There are a large number of important applications of such a result....