Performance Resilience Analysis of Dynamic Feedback Controllers for both Multiplicative and Additive Gain Perturbations

Abstract

In this work, a procedure is presented for performance resilience analysis of continuous-time systems controlled by full-order dynamic feedback compensators. The resilience property is defined in terms of defining maximum perturbations on both the controller and observer gains that will maintain controller and observer eigenvalues in disjoint regions in the complex plane so that the closed loop system will sustain certain performance characteristics. The desired performance is characterized by the response speed and magnitude bounds on the response. Therefore, the intersection of two regions are chosen, vertical strips and sector regions, to guarantee upper and lower bounds on the settling (or response) time and an upper bound on the percent overshoot simultaneously. Maximum allowable gain perturbations are obtained based on the designer’s choices of closed loop eigenvalues and the regions in which eigenvalues remain when the gains are perturbed. The linear matrix inequality technique is used throughout the analysis process. Illustrative examples are included to demonstrate the effectiveness of the proposed methodology.