Data-Driven Stabilization: A Robust Control Approach with Linear Matrix Inequalities

In this paper, we present a novel data-driven approach to stabilize discretized batch reactor systems under the influence of noisy data. By leveraging the framework of Linear Matrix Inequalities (LMIs), our method eliminates the need for explicit system identification, instead utilizing persistently exciting input-output data directly. This enables the design of robust control strategies tailored to the specific dynamics of batch reactors. We address critical control challenges, including state and output feedback stabilization, and demonstrate how data-dependent LMIs ensure stability despite significant uncertainties and measurement noise. Finally, a numerical example is provided to illustrate the efficacy and robustness of the proposed approach. It is shown that whilst the controller ​ designed using LMI satisfies the same criteria provided by the original controller is capable of achieving a faster convergence, better damping and larger robustness. Results from this evaluation show the method stabilizes unstable equilibrium in complex nonlinear environments.