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In this document, a data-driven algorithm to continuous-time observer-based fault isolation from sampled input-output data is considered. The core of the proposed algorithm is to show the advantages with respect previous results such as fault isolation and the capability of consider a special class of nonlinear systems. An example is shown using the algorithm to prove its efficiency as well as a justification of the results.

Fault tolerant control (FTC) seeks to avoid the deterioration of the system at the time that there is a change of one or more parameters outside the limits of tolerance. There is in the literature a set of approaches based on the idea of tracking the nominal trajectory, which have been proved to be effective. However, some of them do not maintain the nominal controller, others, even if they keep it, require meet very demanding existence conditions. This paper proposes a fault recovery using a cascade control structure. The proposed design is based on the nominal trajectory tracking as well, but keeps intact the original control while existence conditions are relaxed. The resulting equivalent controller can be changed according to the performance needs of the system's response to faults. The controller could be defined by using stability regions and LMI tools.

The characterization of frequency response functions for convergent systems is considered in this paper. Besides a couple of approaches available in the literature, this paper is focused on the frequency response function proposed recently for a class of non-linear systems which are called convergent. Using some properties of convergent systems a characterization of a frequency response function based on Fourier series is obtained. This result expands a known result from linear to nonlinear systems and complements the existing results about frequency response functions of nonlinear systems. An example is utilized to show the proposed approach.

A novel non-linear observer for detection of oscillatory faults in commercial airplanes is proposed in this work. Oscillatory Failure detection in airplanes is an important problem because of natural mode excitation and the structural loads they can provoke. A simple and novel non-linear observer with two correction terms is developed. Formal proof of stability and convergence of the observer in the fault free case is provided. The proposed approach satisfies technical requirements of no false alarm, small detection time, detectability of small faults while keeping a simple structure. A test with real measurements is presented to show the efficiency of the proposed observer over the existing techniques.