ABSTRACT In this article, the issue of fault‐tolerant active disturbance rejection control design for interval type‐2 fuzzy stochastic semi‐Markov jump systems with partially unknown transition probabilities is investigated. Primarily, the system model takes into account the impact of linear fractional uncertainties, nonlinear actuator faults, and external disturbances in a unified framework. Moreover, to estimate the disturbances acting on the system model, a proportional‐integral observer‐based improved‐equivalent‐input‐disturbance estimator is configured. Therein, the amalgamation of proportional and integral loops in the observer enhances the estimation precision. Subsequently, making use of knowledge gleaned from the proportional‐integral observer and disturbance estimations, a robust fault‐tolerant active disturbance rejection control is devised, which aids in mitigating the impact of disturbances in the system model and accommodating faults in the actuator component within the semi‐Markov framework. Additionally, a nonparallel distributed compensation methodology is employed, enabling the observer and controller to utilize a different set of membership functions, thus enhancing the robustness and flexibility of the system. Further, with the aid of Lyapunov stability theory and Ito's formula, a sufficient set of conditions is substantiated in the underlying design of linear matrix inequalities to vouch for the central pursuit of the study. Afterward, the gain matrices for the built observer and the intended controller are established by employing the proposed criteria. Ultimately, we deploy the established theoretical insights to the tunnel diode model to showcase its reliability and structural feasibility in practical applications.
Aarthi et al. (Fri,) studied this question.