Observer and fault reconstruction-based control design for interval type-2 fuzzy systems

In this study, the finite-time stabilization and multiple faults reconstruction issues are scrutinized for nonlinear control systems in the presence of time-varying state delay, actuator faults and sensor faults in which the underlying system is approximated by dint of fuzzy approach. To be specific, the interval type-2 (IT2) fuzzy technique is deployed in tandem with a non-parallel distribution compensation scheme to linearize such a faulty system. Further, the existence of unknown inputs in both the system and its output are effectively reconstructed with the aid of IT2 fuzzy-based observer, namely the IT2 fuzzy unknown input (UI) observer. Simultaneously, the designed observer also ensures the reconstruction of system state vectors that are not able to be measured. With the help of this reconstruction information, a fault-tolerant control scheme is established to maintain the performance of the addressed system even in the occurrence of unknown faults. Particularly, in this work, the sampling strategy is incorporated with the developed controller design. Overall, the proposed IT2 fuzzy UI observer-based sampled fault-tolerant controller guarantees the stability of the resulting system within a finite-time duration. Furthermore, the Lyapunov stability theory enables to formulate the delay-dependent adequate constraints in the framework of linear matrix inequalities. On the grounds of established criteria, the relations are also constructed for obtaining the controller and observer gain matrices. Eventually, the simulation study is conducted with two numerical examples to validate the theoretical and practical significance of the developed control procedure.