| Summary: | This paper studies the problem of the finite-time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> control of the blood gases system, presented as a T-S fuzzy model with bounded disturbance during extracorporeal circulation. The aim was to design an observer-based fuzzy controller to ensure that the closed-loop system was finite-time bounded with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> performance. Firstly, different from the existing results, the T-S fuzzy model of a blood gas control system was developed and a new method was given to process the time derivatives of the membership functions. Secondly, based on the fuzzy Lyapunov function, sufficient conditions for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> finite-time boundedness of the system were obtained by using Finsler’s lemma and matrix decoupling techniques. Simulation results are provided to demonstrate the effectiveness of the proposed methodology.
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