Nonlinear H-Infinity Model Reference Controller Design

In this work, a nonlinear and robust controller is proposed for nonlinear uncertain systems by consolidating the H-infinity state feedback control with the model reference control approach. The proposed controller is motivated to achieve a satisfactory transient response by inserting a reference model. The upper and lower linear fractional transformations are constructed in order to extract the structured parametric uncertainties. The controller design procedure is performed based on the small gain theorem. Next, the proposed controller gain matrix is calculated by solving the H-infinity algebraic Riccati equation. The Lyapunov stability analysis is used to show the stability properties of the controlled system. To show the effectiveness of the proposed controller, two types of nonlinear uncertain systems are presented as case studies. Finally, the results demonstrate that the proposed controller is powerful and efficient in compensating the nonlinear uncertain systems and in imposing the asymptotic tracking between the system states and the reference model states.