H_∞ Fault Detection for Two‐Dimensional T‐S Fuzzy Systems in FM Second Model

Abstract

This paper investigates the H∞ fault detection problem for two-dimensional (2D) Takagi-Sugeno (T-S) fuzzy systems in a Fornasini-Marchesini second (FM II) state-space model. Our aim is to develop fault detection filters for the 2D T-S fuzzy system both in the non-fuzzy case and the fuzzy case. Attention is focused on the design of the above two kinds of fault detection filters, which guarantee the fault detection system to be asymptotically stable and to have a prescribed H∞ performance. Sufficient conditions are derived for the existence of such filters in terms of linear matrix inequalities (LMIs), and the corresponding filter synthesis problem then is solved both of the kinds of fault detection filters. Numerical examples are used to demonstrate the effectiveness of the proposed method. Moreover, simulation results show that, under the conditions of reaching the same optimal H∞ performance level and feasible region, the fault detection filter we designed for the fuzzy case has better sensitivity to the fault signal than the one designed for the non-fuzzy case.

Integrated fault detection and control for two‐dimensional Markovian jump systems

“…Then, we will prove that the augmented system (12) has an H ∞ disturbance attenuation level 1 under initial zero boundary condition. Define the following performance index:…”

“…It is obvious that inequality (25) is equivalent to condition (13). Based on Definition 2, it is concluded that the augmented system (12) has an H ∞ disturbance attenuation level 1 . The proof is completed.…”

“…Theorem 1. Given a scalar 1 > 0, the augmented system (12) is stochastically stable with an H ∞ disturbance attenuation level 1…”

“…Corollary 2. Given a scalar 1 > 0, the augmented system (12) is stochastically stable with an H ∞ disturbance attenuation level 1 under uncertainty (33), if there exist matrices Fm , ∀m ∈ S, satisfying conditions (27) and (35), such that the inequality…”

“…[4][5][6] The filtering and control problems have been investigated in other works. [7][8][9][10] The fault detection problem has been considered in some other works, [11][12][13][14] where a finite-frequency fault detection method is proposed in the work of Ding et al, 13 whereas the other studies are considered in full-frequency domain. In the work of Zhao et al, 15 an integrated design method of fault diagnosis subjected to observer information is proposed, and the fault detection rate can be maximized.…”