  We design resilient sparse state-feedback controllers for a linear
time-invariant (LTI) control system while attaining a pre-specified guarantee
on ${\mathcal{H}}_\infty$ performance measure. We leverage a technique from
non-fragile control theory to identify a region of resilient state-feedback
controllers. Afterward, we explore the region to identify a sparse controller.
To this end, we use two different techniques: the greedy method of
sparsification, as well as the re-weighted $\ell_1$ norm minimization. Our
approach 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 sparse
feedback gain design.
