Two-dimensional Roesser Systems Research Articles

Integrated fault detection and control for two-dimensional Roesser systems

This paper addresses the problem of integrated fault detection and control for two-dimensional (2-D) Roesser systems. A fault detection observer/controller is designed to detect faults in low-frequency domain and satisfy some control specifications simultaneously. By the generalized Kalman-Yakubovich-Popov (KYP) lemma and some useful lemmas, this design problem is formulated as a multiobjective optimization problem. A two-step algorithm is proposed to solve this non-convex problem. The effectiveness of the proposed algorithm is illustrated by a numerical example.

Fault Detection for Two-Dimensional Roesser Systems With Sensor Faults

This paper investigates the problem of fault detection for 2-D systems with lock-in-place sensor faults. Our attention is focused on detecting sensor faults in the presence of disturbances. To this end, a fault detection filter is designed, through which a residual signal is generated for both the fault-free and faulty cases. In light of the generalized Kalman–Yakubovich–Popov lemma for 2-D systems and matrix inequality techniques, convex filter design conditions are derived. Based on these conditions, an algorithm is proposed to calculate the parameters of a desired fault detection filter. Moreover, a residual evaluation function and a threshold are proposed for 2-D systems. Finally, an example is employed to illustrate the effectiveness of the proposed fault detection method.

Finite-Frequency Fault Detection for Two-Dimensional Roesser Systems

This paper focuses on the fault detection problem of 2-D systems described by the Roesser model. To detect faults effectively in the presence of disturbances, a fault detection filter is designed to satisfy a finite-frequency $H_{-}$ index and a finite-frequency $H_\infty $ index simultaneously. The corresponding finite-frequency performance analysis conditions are obtained by the aid of the generalized Kalman–Yakubovich–Popov lemma. Then, convex filter design conditions are derived by constructing a hyperplane tangent combined with linear matrix inequality techniques. An algorithm is proposed to construct a desired fault detection filter. Finally, a numerical example is given to show the effectiveness of the proposed method.

L∞-gain performance analysis for two-dimensional Roesser systems with persistent bounded disturbance and saturation nonlinearity

The l∞-gain approach has been an essential tool in one-dimensional system theory. However, limited results have been presented in the literature for the two-dimensional (2-D) l∞-gain approach. This paper investigates the l∞-gain performance for 2-D systems in the Roesser model with persistent bounded disturbance input and saturation nonlinearity. A linear matrix inequality (LMI)-based condition is established to reduce the effect of persistent bounded disturbance input on 2-D systems within a given disturbance attenuation level based on the discrete Jensen inequality, lower bounds lemma, and diagonally dominant matrices. We apply the obtained results to the l∞-gain performance analysis for 2-D digital filters with saturation arithmetic.

Formula omitted] fault detection observer design for two-dimensional Roesser systems

This paper addresses the problem of H−/H∞ fault detection for two-dimensional (2-D) systems with disturbances in Roesser model. A fault detection observer is designed to satisfy a finite frequency H− index and an H∞ index simultaneously. The finite frequency H− index is used to increase the fault sensitivity in low frequency domain while the H∞ index is used to attenuate the effects of disturbances in full frequency domain. By the generalized Kalman–Yakubovich–Popov lemma and some useful lemmas, sufficient design conditions are obtained. An example is given to illustrate the effectiveness of the proposed method.