A new fault detection approach for nonlinear Lipschitz systems with optimal disturbance attenuation level and Lipschitz constant

Abstract

In this paper, a new fault detection approach for nonlinear Lipschitz systems based on observer method is proposed wherein the gain of the observer is obtained by optimal maximized Lipschitz constant and minimized disturbance attenuation level. The FD system is defined as a weighted LMI optimization problem in which the Lipschitz constant and disturbance attenuation level are assumed as decision variables. The projection lemma is used to reduce the conservatism of the proposed FD system. Maximization of the Lipschitz constant will result in robustness of the FD system against parametric and nonlinear uncertainties, while maintaining the fault sensitivity of the FD system and may further eliminate the problem of getting the exact value of the Lipschitz constant in practical applications. A single-link manipulator is provided to demonstrate the effectiveness of the proposed method.