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Reliable H∞ and Passive Fuzzy Observer-Based Sliding Mode Control for Nonlinear Descriptor Systems Subject to Actuator Failure

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Abstract

The present work investigates the Takagi–Sugeno (T–S) fuzzy-based fault-tolerant control for non-linear descriptor systems with uncertainties, external disturbances, and actuator failures. More precisely, the sliding mode control (SMC) approach is employed to develop an observer-based (SMC) strategy for this class of models with the assumption that the sub-model-input matrices can be different. First, an observer is designed to reconstruct the unmeasured states, and a novel integral sliding function, which involves a non-linear term to compensate the matched uncertainty, is formulated. Based on an appropriate fuzzy Lyapunov function, sufficient conditions are established in terms of linear matrix inequality (LMI) to ensure the robust admissibility of the closed-loop system with a satisfactory mixed \(H_\infty \) /passivity performance and determine the sliding function parameters. Then, an adaptive observer-based SMC law is synthesized to adaptively ensure the reachability of the sliding surface and completely compensate for the influence of the previously mentioned factors. Finally, the efficiency of the theoretical findings is shown by the implementation of the proposed reliable SMC controller for practical systems about the pendulum and truck-trailer.

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Abbreviations

TSFS:

Takagi–Sugeno fuzzy systems

FTCS:

Fault tolerant control systems

CLS:

Closed loop system

SMC:

Sliding mode control

PLMI:

Parametrized linear matrix inequality

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Acknowledgements

The authors express their gratitude to the research deanship of Hail University in KSA for their financial support and sponsorship in their pledge for this research (funding scheme (RG-0191315)).

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  1. College of Engineering University of Hail, Po.Box 2440, Hail, Kingdom of Saudi Arabia

    Mourad Kchaou & Houssem Jerbi

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  1. Mourad Kchaou
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  2. Houssem Jerbi
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Correspondence to Mourad Kchaou.

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Kchaou, M., Jerbi, H. Reliable H∞ and Passive Fuzzy Observer-Based Sliding Mode Control for Nonlinear Descriptor Systems Subject to Actuator Failure. Int. J. Fuzzy Syst. 24, 105–120 (2022). https://doi.org/10.1007/s40815-021-01121-x

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