H∞ fuzzy adaptive tracking control design for nonlinear systems with output delays

Tzu Sung Wu, Mansour Karkoub

Research output: Contribution to journalArticle

12 Citations (Scopus)


In this study, we develop fuzzy adaptive tracking control via two-layer fuzzy observers, variable structure systems (VSS), and H control algorithm for nonlinear systems with plant uncertainties, output delays, and external disturbances. The Takagi-Sugeno fuzzy dynamic model with adaptation capability is used to approximate the nonlinear system. When the system states are not available, the states estimated from two-layer fuzzy observers combined with VSS are used to develop the fuzzy adaptive controller. In the first layer, the output delays are partitioned into m+1 equal time intervals to construct the same number of fuzzy observers. The output delayed states in each time interval are used as the premise variables in the IF-THEN rules. The second layer of the fuzzy observers uses output delayed error states as its linguistic variables and it is defuzzified from the first layer. Next, we develop a fuzzy adaptive controller to overcome the nonlinearities, output delayed states, and external disturbances such that H tracking performance is achieved. The Lyapunov criterion and linear matrix inequalities are used to derive the controller. In the present study, our previous method is extended to handle a class of uncertain nonlinear systems with output delays and external disturbances, which is achieved using robust VSS and H control techniques. A magnetic levitation system and inverted pendulum system are used as simulation examples to illustrate the validity and confirm the performance of our proposed scheme.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalFuzzy Sets and Systems
Publication statusPublished - 1 Nov 2014



  • Fuzzy adaptive control
  • Inverted pendulum system
  • Linear matrix inequality
  • Magnetic levitation system
  • Output delay
  • Two-layer fuzzy observer

ASJC Scopus subject areas

  • Artificial Intelligence
  • Logic

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