4.6 Article

Control Synthesis of Hidden Semi-Markov Uncertain Fuzzy Systems via Observations of Hidden Modes

Journal

IEEE TRANSACTIONS ON CYBERNETICS
Volume 50, Issue 8, Pages 3709-3718

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2019.2921811

Keywords

sigma-error mean square stability; hidden semi-Markov chain; stochastic uncertainties; Takagi-Sugeno (T-S) fuzzy system

Funding

  1. National Defense Basic Scientific Research Program of China [JCKY2018603C015]
  2. Cultivation Plan of Major Research Program of Harbin Institute of Technology [ZDXMPY20180101]
  3. Natural Sciences and Engineering Research Council of Canada [RGPIN-2016-05386]
  4. China Scholarship Council [201706120074]

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This paper investigates the stability analysis and fuzzy control problems for a class of discrete-time fuzzy systems with hidden semi-Markov stochastic uncertainties. The nonlinear plant is described via the Takagi-Sugeno (T-S) fuzzy model, and the parameter uncertainties are represented by a hidden semi-Markov chain. Owing to the semi-Markov kernel (SMK), the probability density functions (PDFs) of sojourn time for different modes in describing the stochastic uncertainties can address different types of distributions according to different target modes. A novel Lyapunov function that depends on the hidden mode and the observed mode with the elapsed time is proposed to analyze the stability and the H-infinity performance of the fuzzy system. Then, the sufficient criteria for the elapsed-time-dependent and observed-mode-dependent fuzzy controller are achieved by exploiting the observations of hidden modes, ensuring that the closed-loop system is sigma-error mean square stable with guaranteed H-infinity performance. A cart-pendulum system is used to demonstrate the effectiveness and applicability of the proposed theoretical results.

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