State feedback controller sparsification via a notion of non-fragility

In this paper, a notion of non-fragility is introduced for a state feedback controller which stabilizes a linear time-invariant (LTI) system. Then, lower and upper bounds on such a non-fragility are derived. Based on such derived bounds on non-fragility, a sparsification procedure is proposed to get sparsified state feedback controllers. Investigating the various numerical experiments, it is observed the proposed method is applicable to large-scale systems consisting of thousands of states. Additionally, it is shown in some case studies, the (non-fragilty)-based sparsification procedure outperforms a well-respected existing method in terms of sparsity-performance tradeoff behavior. Also, considering a set of sparse stabilizing state feedback controllers, a tradeoff between upper bound on non-fragility and sparsity level of such state feedback controllers is visualized.

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