Robust $ {H}_{\infty} $ output feedback finite-time control for interval type-2 fuzzy systems with actuator saturation

Chuang Liu; Jinxia Wu; Weidong Yang; Chuang Liu; Jinxia Wu; Weidong Yang

doi:10.3934/math.2022257

AIMS Mathematics

2022, Volume 7, Issue 3: 4614-4635. doi: 10.3934/math.2022257

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Research article

Robust $ {H}_{\infty} $ output feedback finite-time control for interval type-2 fuzzy systems with actuator saturation

1.
School of automation, University of Science and Technology Beijing, Beijing, CO 100083, China
2.
College of Control Science and Engineering, BoHai University, Jinzhou, Liaoning, 121001, China
3.
College of Science, Liaoning University of Technology, Jinzhou, Liaoning, 121001, China

Received: 21 September 2021 Revised: 18 December 2021 Accepted: 20 December 2021 Published: 23 December 2021
MSC : 93C42

The finite-time $ {H_\infty } $ performance of the interval type-2 Takagi-Sugeno fuzzy system (IT2 T-S) in presence of immeasurable states and input saturation is investigated. At first, an observer associated with IT2 T-S states is considered to address the problem of immeasurable states. After that, the input saturation is described based on the polyhedron model, and accordingly, a robust $ {H_\infty } $ observer-based finite-time controller is proposed via non-PDC algorithm. Then, on the basis of the Lyapunov function method and LMIs theory, the sufficient conditions for the finite time stability of fuzzy systems are derived. At last, the feasibility of the designed algorithm is verified by two examples of the nonlinear mass-spring-damping system and tunnel diode circuit system, respectively.
Citation: Chuang Liu, Jinxia Wu, Weidong Yang. Robust $ {H}_{\infty} $ output feedback finite-time control for interval type-2 fuzzy systems with actuator saturation[J]. AIMS Mathematics, 2022, 7(3): 4614-4635. doi: 10.3934/math.2022257

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Abstract

The finite-time $ {H_\infty } $ performance of the interval type-2 Takagi-Sugeno fuzzy system (IT2 T-S) in presence of immeasurable states and input saturation is investigated. At first, an observer associated with IT2 T-S states is considered to address the problem of immeasurable states. After that, the input saturation is described based on the polyhedron model, and accordingly, a robust $ {H_\infty } $ observer-based finite-time controller is proposed via non-PDC algorithm. Then, on the basis of the Lyapunov function method and LMIs theory, the sufficient conditions for the finite time stability of fuzzy systems are derived. At last, the feasibility of the designed algorithm is verified by two examples of the nonlinear mass-spring-damping system and tunnel diode circuit system, respectively.

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