Robust H₋/H_∞ fault detection observer design for descriptor-LPV systems with unmeasurable gain scheduling functions

Abstract

This paper addresses a design of a fault detection observer (FDO) for descriptor linear parameter varying (D-LPV) systems. In contrast with the conventional approach for D-LPV systems, the gain scheduling functions (GSF) are considered unmeasurable. The FDO is investigated in the H₋/H_∞ index framework in order to minimise the effects of the disturbance and maximise the effect of faults on the residuals, and minimise the error caused by the unmeasurable GSF. The stability is guaranteed based on a Lyapunov approach. Sufficient conditions for the existence of the FDO are established in terms of linear matrix inequalities. The effectiveness of the proposed method is illustrated by means of a simulation example.

Keywords:

• fault detection
• descriptor systems
• linear parameter varying
• H∞/H₋ index
• unmeasurable gain scheduling functions

Acknowledgements

This work is supported by CONACyT (Consejo Nacional de Ciencia y Tecnología), Mexico. The supports is gratefully acknowledged. The authors would like to thank Professor Johan Löfberg for his advice and help in the YALMIP Google group to solve the LMIs system.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The descriptor approach consists in transforming a standard system into a descriptor system to estimate sensor faults.