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We design resilient sparse state-feedback controllers for a lineartime-invariant (LTI) control system while attaining a pre-specified guaranteeon ${\mathcal{H}}_\infty$ performance measure. We leverage a technique fromnon-fragile control theory to identify a region of resilient state-feedbackcontrollers. Afterward, we explore the region to identify a sparse controller.To this end, we use two different techniques: the greedy method ofsparsification, as well as the re-weighted $\ell_1$ norm minimization. Ourapproach highlights a tradeoff between the sparsity of the feedback gain,performance measure, and fragility of the design. To best of our knowledge,this work is the first framework providing performance guarantees for sparsefeedback gain design.

Resilient Sparse Controller Design with Guaranteed Disturbance Attenuation