LMI-Based Robust $\mathrm{H}_{2}$ State Feedback Stabilizer for Uncertain Nonlinear Systems with External Disturbances

This paper proposes a linear matrix inequality (LMI)-based state feedback stabilizer for uncertain nonlinear systems with external disturbances. LMIs are formulated to design a robust <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{H}_{2}$</tex> control scheme that ensures system performance and stability under uncertainties and time-varying disturbances. The system's asymptotic stability is established using the Lyapunov theory and based on LMI formulations. The stabilization and disturbance rejection capabilities of the proposed approach were assessed using an inverted pendulum system subject to external disturbances. Both numerical and experimental validations were carried out. The obtained results as well as a comparison analysis with another approach confirmed the performance and of the proposed design. Among the major advantages of the proposed LMI-based strategy are its efficient and straightforward design, independent of system order and complexity.