Almost all robust properties of linear systems can be related directly to properties of the controllability or observability Gramian. A model-based fuzzy controller for a class of uncertain nonlinear systems will be developed in this paper to achieve a common observability Gramian. Design of a model-based fuzzy controller begins by assigning a certain common observability Gramian. The nonlinear systems considered in this paper are represented by Takagi-Sugeno fuzzy models. An application to the inverted pendulum system will be given to demonstrate the effects of the present design method.
1.
Takagi
, T.
, and Sugeno
, M.
, 1985
, “Fuzzy Identification of Systems and Its Applications to Modeling and Control
,” IEEE Trans. Syst. Man Cybern.
, SMC-15
, pp. 116
–132
.2.
Boyd, S., et al., 1994, Linear Matrix Inequalities in Systems and Control Theory, SIAM, Philadelphia, PA.
3.
Wang, H. O., and Tanaka, K., 1996, “An LMI-based Stable Fuzzy Control of Nonlinear Systems and Its Application to Control of Chaos,” Proc. 5th IEEE Int. Conf. on Fuzzy Systems, New Orleans, LA, pp. 1433–1438.
4.
Wang
, H. O.
, Tanaka
, K.
, and Griffin
, M. F.
, 1996
, “An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues
,” IEEE Trans. Fuzzy Syst.
, 4
, pp. 14
–23
.5.
Moore
, B. C.
, 1981
, “Principle Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction
,” IEEE Trans. Autom. Control
, AC-26
, pp. 17
–32
.6.
Wicks
, M. A.
, and Decarlo
, R. A.
, 1990
, “Gramian Assignment Based on the Lyapunov Equation
,” IEEE Trans. Autom. Control
, 35
, pp. 465
–468
.7.
Yasuda
, K.
, and Skelton
, R. E.
, 1991
, “Assigning Controllability and Observability Gramians in Feedback Control
,” J. Guid. Control Dyn.
, 14
, pp. 878
–885
.8.
Campbell, S. L., and Meyer, C. D., 1991, Generalized Inverses of Linear Transformations, Dover, New York.
9.
Chung
, H. Y.
, and Chang
, W. J.
, 1991
, “Constrained Variance Design for Bilinear Stochastic Continuous Systems
,” IEE Proc.-D: Control Theory Appl.
, 138
, pp. 145
–150
.10.
Barnett
, S.
, and Storey
, C.
, 1967
, “Analysis and Synthesis of Stability Matrices
,” J. Diff. Eqns.
, 3
, pp. 414
–422
.11.
Cannon, R. H., 1967, Dynamics of Physical Systems, McGraw-Hill, New York.
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