Actuator fault estimation based on a proportional-integral observer with nonquadratic Lyapunov functions

This work proposes a proportional-integral fault estimation observer for nonlinear systems by means of convex structures. Unlike the traditional approaches that consider quadratic Lyapunov functions, this work employs nonquadratic ones. As a result, less conservative conditions in the form of linear matrix inequalities are obtained. Furthermore, an H∞ performance is employed in order to ensure robustness against sensor noise and disturbances; thus, the designed observer estimates both the state and the actuator faults even in the presence of disturbances. The performance of the proposed methodology is illustrated through a numerical example and a three-tank hydraulic system.