Generalised H2 controller synthesis for uncertain discrete-time fuzzy systems via basis-dependent Lyapunov functions

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Generalised H2 controller synthesis for uncertain discrete-time fuzzy systems via basis-dependent Lyapunov functions

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The generalised H2 control problem is investigated for a class of discrete-time fuzzy systems with uncertainties. The uncertain fuzzy dynamic model is used to represent a class of uncertain discrete-time complex nonlinear systems which include both linguistic information and system uncertainties. Using basis-dependent Lyapunov functions an H2 control design approach is developed. It is shown that the controller can be obtained by solving a set of linear matrix inequalities. It is also shown that the basis-dependent results are less conservative than the basis-independent ones. Numerical examples including a discrete chaotic Lorenz system are also given to demonstrate the applicability of the proposed approach.

Inspec keywords: nonlinear control systems; fuzzy control; uncertain systems; control system synthesis; chaos; linear matrix inequalities; large-scale systems; discrete time systems; Lyapunov methods

Other keywords: discrete chaotic Lorenz system; linear matrix inequalities; system uncertainties; uncertain fuzzy dynamic model; Lyapunov functions; linguistic information; uncertain discrete-time fuzzy systems; H2 controller synthesis

Subjects: Fuzzy control; Multivariable control systems; Stability in control theory; Nonlinear control systems; Discrete control systems; Control system analysis and synthesis methods

References

    1. 1)
      • Guerra, T.M., Perruquetti, W.: `Nonquadratic stabilisation of discrete Takagi–Sugeno fuzzy models', Proc. of 2001 IEEE Int. Conf. on Fuzzy Systems, April 2001, p. 1271–1274.
    2. 2)
      • Jadbabaie, A., Jamshidi, M., Titli, A.: `Guaranteed-cost design of continuous-time Takagi–Sugeno fuzzy controllers via linear matrix inequalities', Proc. of IEEE World Congress on Computational Intelligence, 1998, Anchorage, AK, p. 268–273.
    3. 3)
      • Y.Y. Cao , P.M. Frank . Robust H∞ disturbance attenuation for a class of uncertain discrete-time fuzzy systems. IEEE Trans. Fuzzy Syst. , 4 , 406 - 415
    4. 4)
      • M.C. de Oliveira , J.C. Geromel , J. Bernussou . Extended H∞ and H2-norm characterisations and controller parametrisations for discrete-time systems. Int. J. Control , 9 , 666 - 679
    5. 5)
      • D. Choi , P. Park . H∞ state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting-dependent Lyapunov functions. IEEE Trans. Fuzzy Syst. , 271 - 278
    6. 6)
      • T. Tanaka , T. Ikeda , H.O. Wang . Robust stabilisation of a class of uncertain nonlinear systems via fuzzy control: Quadratic stability, H∞ control theory, and linear matrix inequlities. IEEE Trans. Fuzzy Syst. , 1 - 13
    7. 7)
      • M.A. Rotea . The generalized H2 control problem. Automatica , 373 - 383
    8. 8)
      • L. Xie . Output feedback H∞ control of systems with parameter uncertainty. Int. J. Control , 4 , 741 - 750
    9. 9)
      • S.S. Zhou , J. Lam . Robust stabilisation of delayed singular systems with linear fractional parametric uncertainties. Circuits Syst. Signal Process. , 6 , 579 - 588
    10. 10)
      • M.W. Haddad , S.D. Bernstein . Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis. IEEE Trans. Automat. Control , 3 , 536 - 543
    11. 11)
      • T. Tanaka , M. Sugeno . Stability analysis and design of fuzzy control system. Fuzzy Sets Syst. , 2 , 135 - 156
    12. 12)
      • L. El Ghaoui , G. Scorletti . Control of rational systems using linear fractional representtions and linear matrix inequalities. Automatica , 9 , 1273 - 1284
    13. 13)
      • H.J. Lee , J.B. Park , G. Chen . Robust fuzzy control of nonlinear systems with parametric uncertainties. IEEE Trans. Fuzzy Syst. , 2 , 369 - 379
    14. 14)
      • S.G. Cao , N.W. Rees , G. Feng . Analysis and design for a class of complex control systems. Part II: Fuzzy controller design. Automatica , 1029 - 1039
    15. 15)
      • S.G. Cao , N.W. Rees , G. Feng . Analysis and design for a class of complex systems. Part I: Fuzzy modelling and identification. Automatica , 6 , 1017 - 1028
    16. 16)
      • L. Guo . H∞ output feedback control for delay systems with nonlinear and parametric uncertainties. IEE Proc. Control Theory Appl. , 3 , 226 - 236
    17. 17)
      • G. Feng , D. Sun . Generalized H2 controller synthesis of uncertain fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans. Circuits Syst. I , 1843 - 1850
    18. 18)
      • S.G. Cao , N.W. Rees , G. Feng . H∞ control of uncertain dynamical fuzzy discrete-time systems. IEEE Trans. Syst., Man. Cybern. , 802 - 812
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