Sensor fault detection based on L∞ interval observer for uncertain continuous-time switched linear systems

In this paper, we address the challenge of designing an interval Fault Detection (FD) method for continuous-time Switched Linear Systems (SLS) in the Unknown But Bounded Error (UBBE) context. The considered systems are subject to unknown but bounded disturbances (state and output disturbances) in predefined intervals. A novel technique is developed to construct residual framers using interval observer with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> criterion. The proposed approach is used to supply more degrees of design freedom and to achieve accurate FD results. The design conditions of the proposed FD interval observer are provided in terms of Linear Matrix Inequalities (LMIs) adopting a common quadratic Lyapunov function, under an arbitrary switching signal. Furthermore, a fault detection decision is proposed to indicate the presence of faults using interval analysis. The performances of the proposed approach is highlighted on illustrative examples and comparative studies.