Proportional-Difference Observer-Based Fault Estimation Design for Discrete-Time Nonlinear Singular Systems With Disturbances

This article presents a robust fault reconstruction scheme for a class of discrete-time nonlinear singular systems with disturbances. The Lipschitz condition is utilized to describe the nonlinearity under investigation. To effectively estimate multiple types of faults such as time-varying faults and constant ones, a brand-new proportional-difference (PD) observer design method is established. What is worth mentioning is that all the gains of PD observer can be calculated at the same time by our method instead of manually selecting some gains and then solving other gains as has been done in the pertinent literature, which serves as a pioneering attempt for the similar design. Besides, by using the Lyapunov theory, less conservative linear matrix inequalities (LMIs) criteria with slack scalars and matrices are obtained to ensure that error systems are robust stability with the prescribed $H_{\infty }$ performance. Finally, two examples on RC circuits and tanks level control models are presented to prove the superiority and practicability of the proposed fault estimation procedure. Note to Practitioners—This article is motivated to realize the PD observer-based fault estimation design of nonlinear singular systems in the discrete-time domain even if there are external disturbances and faults in the system model. The practical significance of this article is mainly twofold. First, since aerospace engineering, power systems, electrical circuit networks and industrial process systems, etc. can be modeled by singular systems, to get closer to reality, it is of great importance to research such systems especially in the presence of nonlinearities and disturbances. Second, the increasing complexity of modern control systems has led to the prevalence of faults in all engineering environments. What is more, the faults often occur in many forms and not just in the form of constant faults in practice. In this case, the achievement of fault estimation for multiple types of faults makes our method applicable in actual engineering, especially in the application of active fault-tolerant control.