In this paper, we devise sampled-data state-feedback controllers for uncertain linear systems that ensure robust stability and \(\mathcal {H}_\infty \) performance. We model the closed-loop system as a hybrid linear dynamic system with polytopic or interval uncertainties, capturing continuous and discrete-time behaviours in a unified framework. This approach avoids the proliferation of uncertain parameters typically encountered in discretization methods. Using this hybrid model, we derive computationally tractable control design conditions that guarantee an upper bound for the associated closed-loop \(\mathcal {H}_\infty \) norm. Our formulation enables designers to select between interval methods that offer computational efficiency for systems with numerous independent uncertainties, or polytopic methods that provide less conservative results at higher computational cost. Numerical examples with detailed simulation verification demonstrate the effectiveness of our proposed techniques and validate the theoretical performance guarantees across the entire uncertainty space.
