H∞/H− Fault Detection for Discrete T-S Fuzzy Systems with Unmeasurable Premise Variables
1. School of Science, Dalian Jiaotong University, Dalian 116028, China
2. School of Electric Engineering and Automation, Dalian Jiaotong University, Dalian 116028, China
| Abstract: | In this paper, we study the fault diagnosis problem for a class of discrete nonlinear systems with unmeasurable premise variables, which are Takagi-Sugeno (T-S) models. The studied T-S structure can simplify the computation by using rules containing local nonlinearities to reduce the number of rules in the model. In designing the fault detection observer, the main consideration is the unknown input signal, while maximizing the effect of actuator failure on the generated residuals in order to minimize the impact of uncertainty on the system performance. The H- performance index of residual-to-fault sensitivity and the H∞ performance index of residual-to-unknown-input robustness are described, and the design problem of a robust fault detection observer is described as an optimal design problem satisfying H∞/H-. The unmeasurable premise variables are compared to the case of measurable premise variables, which can represent larger nonlinear systems. Then, a new iterative linear matrix inequality (LMI) algorithm and convex optimization technique are proposed to solve the optimal observer gain matrix by giving the existence conditions of the fault detection observer. Finally, the effectiveness of the method is verified by numerical examples, and the fault detection observer designed by this method is highly sensitive to faults and robust to unknown inputs. |
| Keywords: | Discrete-Time T-S Fuzzy System; Non-measurable Premise Variables; Fault Diagnosis; H∞/H- Performance Index |
| DOI: | 10.57237/j.se.2023.05.001 |
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Received: 13 June 2023
Accepted: 14 July 2023
Published Online: 9 October 2023
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