Observer-based finite-time fuzzy H ∞ control for systems with stochastic actuator and sensor faults

This study addresses the challenge posed by the unmeasurable system state by proposing the utilisation of a fuzzy observer. Subsequently, a fuzzy controller is formulated based on the estimated states to effectively address the issue of finite-time fuzzy control for a nonlinear system affected by actuator and sensor faults. Specifically, the nonlinear system, incorporating external disturbances, is represented utilising the Takagi-Sugeno methodology, with actuator and sensor faults modelled as a Markov stochastic process. Following this, an observer-based fuzzy sampled-data controller is designed employing the Lyapunov stability theorem. Through the application of the integral inequality technique, less conservative conditions are established to ensure the finite-time stability of the stochastic fuzzy system and to satisfy the H∞ performance criterion. Finally, the efficacy of the proposed approach is validated through numerical simulations on two examples: a mass–spring–damper system and the Fisher equation.