Abstract
We investigate robust fault-tolerant control pertaining to Takagi–Sugeno (TS) fuzzy nonlinear systems with bounded disturbances, actuator failures, and time delays. A new fault model based on a sampled-data scheme that is able to satisfy certain criteria in relation to actuator fault matrix is introduced. Specifically, we formulate a reliable controller with state feedback, such that the resulting closed-loop-fuzzy system is robust, asymptotically stable, and able to satisfy a prescribed H∞ performance constraint. Linear matrix inequality (LMI) together with a proper construction of the Lyapunov–Krasovskii functional is leveraged to derive delay-dependent sufficient conditions with respect to the existence of robust H∞ controller. It is straightforward to obtain the solution by using the MATLAB LMI toolbox. We demonstrate the effectiveness of the control law and less conservativeness of the results through two numerical simulations.
Highlights
Published: 8 December 2021Since most real-world control systems require nonlinear modelling, it is crucial to design and develop appropriate controllers for nonlinear systems
We describe a nonlinear system as ẋ (t) z(t) =
For given positive scalars τo, τM, λ1 and unknown actuator fault matrix F, nonlinear continuous-time fuzzy System (12) is robust and asymptotically stable pertaining to sampled-data feedback control (11) with a given disturbance attenuation level γ > 0, if there exist positive definite symmetric matrices P, Q, R, Ŝ, Û, any matrix Yη with appropriate dimension and positive scalars e, e1 in such a way that satisfies the following Linear matrix inequality (LMI): Φη =
Summary
Since most real-world control systems require nonlinear modelling, it is crucial to design and develop appropriate controllers for nonlinear systems. Sufficient stabilization conditions for dynamical systems with sampled-data control through input delays have been developed ([9,10,11]) Both stability and control performance requirements, Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. To the best of our knowledge, research on sampled-data-based feedback reliable control with nonlinear TS fuzzy systems having actuator failures and time delays is yet to be comprehensively examined. This is the motivation of our current study, which makes the following contributions. (iii) Demonstration and evaluation of effectiveness pertaining to the proposed method with two numerical simulations
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