A fault detection observer design for LPV systems in finite frequency domain

Abstract

This paper addresses the fault detection observer design problem for linear parameter-varying systems. Two finite frequency performance indexes are introduced to measure the fault sensitivity and the disturbance robustness. First, the H₋ index fault sensitivity condition in finite frequency domain is obtained by generalised Kalman–Yakubovich–Popov lemma and new linearisation techniques. Then, with the aid of Kalman–Yakubovich–Popov lemma and projection lemma, the stability and robustness conditions are derived. It turns out that the non-convexity problem which is caused by dealing with the above three conditions can be translated into a bilinear matrix inequality optimisation problem by increasing the dimensions of slack variable matrix. An iterative linear matrix inequality algorithm is proposed to get the solution. The effectiveness of the filter is shown via three numerical examples.

Keywords:

• fault detection
• H₋ index
• linear parameter-varying systems
• generalised Kalman–Yakubovich–Popov lemma
• linear matrix inequalities

Acknowledgements

The authors greatly appreciate the editor, associate editor and anonymous referees for their insightful comments and suggestions that have significantly improved this article.

Additional information

Funding

This paper is partly supported by the National Science Foundation of China [grant number 61025016], [grant number 61473183],[grant number 61034008],[grant number 61221003], [grant number 61471275]; Program of Shanghai Subject Chief Scientist [grant number 14XD1402400]; and SJTU M&E Joint Research Foundation [grant number YG2013MS04]; Key program of Hubei Provincial Department of Education [grant number Z20081102], [grant number D20141104].