Robust Reliable H∞ Control for a Class of Nonlinear Perturbed Systems with Electrical Application: An LMI Approach

Abstract

AbstractThis paper discusses the robust feedback control for a class of nonlinear polynomial systems with H∞ robustness performance. The studied systems are described by perturbed polynomial models based on the Kronecker product and the Kronecker power of the state vector. The proposed nonlinear feedback control scheme is developed to provide the practical stability of the closed loop system using the well-known second Lyapunov method with quadratic function. A sufficient condition for robust stabilization and H∞ control performance is given such that ultimately bounds on the controlled system trajectories are ensured and at the same time the effect of external disturbance on control performance is attenuated to a minimum level. The developed control approach is formulated as a minimization problem and derived in the form of Linear Matrix Inequalities (LMIs). To asses the performances of the proposed control method through numerical simulations, a power electrical application is chosen to provide the effectiveness of the proposed methodology.