Finite-Frequency H-/H∞ Fault Detection for Discrete-Time T-S Fuzzy Systems With Unmeasurable Premise Variables

• Published in: IEEE transactions on cybernetics Vol. 51; no. 6; pp. 3017 - 3026
• Main Authors: Zhou, Meng, Cao, Zhengcai, Zhou, MengChu, Wang, Jing
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Attenuation; Discrete time systems; Discrete-time T–S fuzzy systems; Fault detection; finite-frequency <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H - index; Fuzzy systems; Indexes; Linear matrix inequalities; Nonlinear systems; Observers; Robot arms; Scalars; unmeasurable premise variable
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2019.2915050

This paper investigates a finite-frequency <inline-formula> <tex-math notation="LaTeX">H_{-}/H_{\infty } </tex-math></inline-formula> fault detection method for discrete-time T-S fuzzy systems with unmeasurable premise variables. To minimize the effect of uncertainties on system performance and maximize that of actuator faults on the generated residual, both the <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> disturbance attenuation index and finite-frequency <inline-formula> <tex-math notation="LaTeX">H_{-} </tex-math></inline-formula> fault sensitivity index are utilized. Since the premised variables are unmeasurable, the existing generalized Kalman-Yakubovich-Popov lemma cannot be directly extended to these nonlinear systems. In this paper, the conditions of allowing one to design the proposed <inline-formula> <tex-math notation="LaTeX">H_{-}/H_{\infty } </tex-math></inline-formula> fault detection observer are established and transformed into linear matrix inequalities. Some scalars and slack matrices are introduced to bring extra degrees of freedom in observer design. Finally, a single-link robotic manipulator model is utilized to illustrate that the proposed technique can detect faults with smaller amplitude than that required by a normal <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> observer technique.