H∞ fault estimator for parabolic systems with time-varying delays and sensor faults.

In this paper, an observer based H ∞ fault estimation of second order partial differential equation (PDE) is investigated. A second order PDEs with time-varying delays, external disturbances and output sensor fault is considered. With the help low-pass filter, fault in the considered PDE system is characterized. The fault estimator is designed by using the Lyapunov theory and linear matrix inequalities (LMIs) approach. The sufficient conditions in the form of LMIs are developed to ensure the resulting error system is exponentially stable with ℋ ∞ disturbance attenuation level. The designed estimator gain matrices can be easily determined by using MATLAB LMI toolbox. Finally, numerical example is provided to illustrate the effectiveness and advantages of the obtained results.