Generalised finite-frequency KYP lemma in delta domain and applications to fault detection

Abstract

This article generalises the Kalman--Yakubovi[cbreve]--Popov (KYP) lemma in delta domain to treat some conditions on different restricted frequency ranges. The frequency ranges are characterised by two quadratic forms. This characterisation encompasses low/middle/high frequency conditions for delta operator systems. By utilising the obtained delta domain generalised KYP lemma, a fault detection filter design problem is dealt with for delta operator systems in finite-frequency domain. The fault detection filter design problem is formulated as a two-objective optimisation algorithm with H ₋ and H _∞ performance indexes. A numerical example is given to illustrate the effectiveness and potential for the developed techniques.

Keywords:

• Kalman--Yakubovi[cbreve]--Popov lemma
• delta operator system
• finite-frequency domain
• fault detection
• linear matrix inequality (LMI)

Acknowledgements

The work of Y. Xia was supported by the National Natural Science Foundation of China under Grant 60974011, Program for New Century Excellent Talents in University of Peoples Republic of China (NCET-08-0047), the Ph.D. Programs Foundation of Ministry of Education of China (20091101110023), Program for Changjiang Scholars and Innovative Research Team in University, and Beijing Municipal Natural Science Foundation (4102053) and 973 project (613121010203).