Fault detection for switched systems with all subsystems unstable

Abstract

This study focuses on the H ∞ / H − fault detection for a switched system with all subsystems unstable. Firstly, to eliminate the instability brought by unstable modes, the average dwell time method is introduced to generate the time-driven switching signal. Under the effect of the signal, the exponential stability is guaranteed. Afterwards, the authors utilise the Luenberger observer as the fault detector. Considering the unobservable conditions (A, C), this study gives the new solution to the observer design. Taking the disturbance robustness and fault sensitivity into account, they borrow the mixed H ∞ / H − performance index from the existing researches. Sufficient conditions are supplied to ensure the system is exponentially stable with mixed H ∞ / H − performance using linear matrix inequalities. Finally, examples are provided to prove the validity and effectiveness of the proposed switching method and designed fault detector.