Delayed State Feedback Controller Design for Inverted Pendulum Using T-S Fuzzy Modeling: An LMI Approach

  • Rupak DattaEmail author
  • Rajeeb Dey
  • Baby Bhattacharya
  • Abanishwar Chakrabarti
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 757)


Balancing inverted pendulum along a vertical position with or without cart is a benchmark control problem owing to the fact that out of two equilibrium points, inverted one is open-loop unstable. In this paper, an attempt has been made to stabilize the system with delayed state feedback control strategy using T-S fuzzy modeling in an linear matrix inequality (LMI) framework. Then, by Lyapunov–Krasovskii (L-K) theory, it is proved that the closed-loop system is locally asymptotically stable around its unstable equilibrium point. The result of the control design is validated through closed-loop simulation carried out in MATLAB Simulink.


Inverted pendulum Takagi-Sugeno (T-S) fuzzy model State feedback control Linear matrix inequality (LMI) 


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Rupak Datta
    • 1
    Email author
  • Rajeeb Dey
    • 2
  • Baby Bhattacharya
    • 1
  • Abanishwar Chakrabarti
    • 3
  1. 1.Department of MathematicsNIT AgartalaAgartalaIndia
  2. 2.Department of Electrical EngineeringNIT SilcharSilcharIndia
  3. 3.Department of Electrical EngineeringNIT AgartalaAgartalaIndia

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