Non-Fragile H∞ Order Reduction of LTI Controllers

The eigenvalue perturbation theorem is used to propose a convex fragility criterion with application to control system design. The criterion can be considered as a non-normality measure of the controller state-space matrix. Non-normality of a matrix is defined as its distance to the nearest real normal matrix within a convex normal subspace. Based on the criterion, an $\mathcal {H}_{\infty }$ method for the order reduction of linear time-invariant (LTI) controllers is developed which leads to non-fragile reduced order controllers.