Analysis of Performance Resilience for Discrete-Time Systems With Both Multiplicative and Additive Control Gain Perturbations

In this work, a procedure is presented for performance analysis of the resilience property of discrete-time systems with perturbed controller and observer gains. The resilience property is defined in terms of both multiplicative and additive perturbations on the gains so that the closed loop eigenvalues do not leave a specified region in the complex plane. In this work, this region is chosen as a disk in the unit circle. Maximum gain perturbation bounds can be obtained based on the designer’s choices of controller eigenvalue region. The linear matrix inequality technique is used throughout the analysis process. Illustrative examples are included to demonstrate the effectiveness of the proposed methodology. The observer counterpart of the results is also provided in an appendix.