OTIMIZAÇÃO RESTRITA VIA CONTROLE H ∞ COM INCERTEZAS NÃO ESTRUTURADAS USANDO DESIGUALDADES MATRICIAIS LINEARES

In this research work, we employ Linear Matrix Inequalities (LMIs), a powerful mathematical tool used in robust control theory, which is based on Lyapunov’s theorem. This study presents both analysis and synthesis of robust H ∞ control through the classical state feedback technique for linear time-invariant systems subject to unstructured uncertainties. The objective of this work is to design a controller that remains robust even in the presence of uncertainties using the H ∞ norm. By applying the Schur Complement and the Bounded Real Lemma, we formulate a constrained optimization problem based on these LMIs. With the obtained state feedback gain, the system output exhibited an overshoot before stabilizing. In this H ∞ norm evaluation, we are not primarily concerned with performance but rather with stability, as the behavior is typical of an optimal or robust controller where control effort is initially higher to minimize settling time. The H ∞ controller designed via LMIs stabilizes the system with smooth convergence and no overshoot. The calculated gain K balances performance and robustness, as evidenced by the state responses and control signal, along with the absence of oscillations in u(t). The results demonstrate the effectiveness of the proposed method in achieving robust stability while maintaining satisfactory dynamic performance.