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Various control schemes rely on a solution of a convex optimization probleminvolving a particular robust quadratic constraint, which can be reformulatedas a linear matrix inequality using the well-known $\mathcal{S}$-lemma.However, the computational effort required to solve the resulting semidefiniteprogram may be prohibitively large for real-time applications requiring arepeated solution of such a problem. We use some recent advances in robustoptimization that allow us to reformulate such a robust constraint as a set oflinear and second-order cone constraints, which are computationally bettersuited to real-time applications. A numerical example demonstrates a hugespeedup that can be obtained using the proposed reformulation.

Improving Tractability of Real-Time Control Schemes via Simplified $\mathcal{S}$-Lemma