Evaluate the performance of the systems with uncertainties

Robustness is considered as a system property of stability being unaffected by perturbations, as far as possible. However, the performance of the closed-loop systems will be degraded in order to reach the robustness of the control. The performance of the system with uncertainties is defined as “perturbed cost” of feedback control. The aim of this paper is to establish the relationship between the optimal cost of the system and the cost perturbed by the system uncertainties. The bounds on the ratio of optimal cost to the perturbed cost can be considered as the “distance” between optimal control and a linear feedback control stabilizing the system