Fault detection observer design for 2-D continuous nonlinear systems with finite frequency specifications. (January 2019) - Duan, Zhaoxia; Ghous, Imran; Huang, Shipei; Fu, Jinna
Abstract: This research studies the problem of fault detection observer design for two-dimensional (2-D) continuous-time nonlinear systems in Takagi–Sugeno (T–S) form. Finite frequency (FF) specifications are used to design the observers, which makes observer designing different from previously proposed 2-D detection observers. Faults and disturbances are considered to be dominated in two different FF domain intervals. Fault sensitivity and disturbance robustness are measured by two FF performance indices, respectively. The aim of this paper is to design fault detection observers such that the residual error system has the sensitivity to faults and the desired robustness to disturbances. Sufficient conditions for the existence of a desired fault detection fuzzy observer are established in terms of linear matrix inequalities (LMIs). Simulation results indicate that faults can be detected effectively using the proposed method. Highlights: H − and H ∞, finite frequency (FF) performance indices are firstly defined to measure the sensitivity against fault and the disturbance robustness, which contain the frequency information of fault and disturbance inputs and cover the FF H − and H ∞ indices defined in Wang et al. (2015) for linear 2-D continuous systems as special cases. Based on the defined FF H − and H ∞ performance indices, sufficient conditions for the existence of fault detection observers are developed to ensure that the residual error system is stable and has desired FF H − and H ∞ performance levels. A systematic fault detection scheme is proposed by converting the corresponding fault detection observer design into a convex optimization problem via introducing some auxiliary fixed matrix variables.