Observer-based detection and isolation of permanent sensor faults in a class of uncertain switched affine systems

This paper develops a robust fault detection and isolation (FDI) strategy for a class of uncertain continuous-time switched affine systems when the system state is not fully available for measurement, and all system sensors are prone to permanent abrupt bounded faults. The FDI strategy is obtained by designing a number of FDI devices equal to the number of sensors. First, we give linear matrix inequalities conditions to design a bank of full-state Luenberger observers in a pseudo-dedicated scheme with guaranteed $S_{-}$ and $L_{\infty }$ performances to work as residual error generators (REGs). In the sequence, considering an extension of the concepts of weak and strong detectability and novel concepts of weak and strong isolation, residual evaluation functions are defined, and threshold functions are designed considering the gains and parameters obtained in the REG design, taking into consideration the smallest fault magnitude to be detected to achieve a mixed $S_{-}/L_{\infty }$ performance. An Algorithm to determine a piecewise constant threshold function is proposed to obtain less conservative constraints in the optimization problem. Furthermore, parameter-tuning algorithms are proposed to obtain local optima thresholds and REGs to satisfy weak isolation conditions over a range of uncertainties. Finally, a Cuk DC–DC converter is considered to demonstrate the effectiveness of the proposed approach.