Resilient H∞ Control Design for Discrete‐Time Uncertain Linear Systems: An Auxiliary System Transformation Approach

This paper studies the resilient (non-fragile) H∞ output-feedback control design for discrete-time uncertain linear systems with controller uncertainty. The design considers parametric norm-bounded uncertainty in all state-space matrices of the system, output and controller equations. The paper shows that the resilient H∞ output-feedback control problem is equivalent to a scaled H∞ output-feedback control problem of an auxiliary system without any system or controller uncertainty. Using the existing optimal H∞ design to solve the auxiliary system, the design guarantees that the resultant closed-loop systems are quadratically stable with disturbance attenuation γ for all admissible system and controller uncertainties. A numerical example is given to illustrate the design method and its benefits.