# Design of a robust observer-based fault detection for a class of switched discrete-time linear systems

## TL;DR

This paper presents a robust hybrid observer design for switched discrete-time linear systems that effectively detects faults despite unknown inputs and modeling errors, using an optimized LMI-based approach.

## Contribution

It introduces a novel observer synthesis method for unknown active modes in switched systems, balancing robustness and fault sensitivity through iterative LMI optimization.

## Key findings

- The proposed observer effectively detects faults in numerical simulations.
- The method achieves a good trade-off between robustness and sensitivity.
- LMI-based optimization improves observer performance.

## Abstract

This work addresses the design of a robust hybrid observer for discrete-time switched linear systems subject to unknown inputs and modeling errors. The observer herein proposed is synthesized, for the case when the active mode is unknown and in the purpose of robust fault detection. We'll show that a suitable trade-off between the robustness to unknown inputs and sensitivity to faults can be obtained through a performance index. The latter is optimized using an iterative LMI solution procedure. The efficiency of the proposed approach is illustrated by a numerical example.Keywords: Switched Systems, Fault Detection, Observer design, optimization, Linear Matrix Inequality (LMI)

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Source: https://tomesphere.com/paper/1902.06448