This paper addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties. The Takagi-Sugeno (T-S) fuzzy model is adopted for fuzzy modeling of the nonlinear system. Two cases of the T-S fuzzy system with parametric uncertainties, both continuous-time and discrete-time cases are considered. In both continuous-time and discrete-time cases, sufficient conditions are derived for robust stabilization in the sense of Lyapunov asymptotic stability, for the T-S fuzzy system with parametric uncertainties. The sufficient conditions are formulated in the format of linear matrix inequalities. The T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a test bed. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic Lorenz system.
Bibliographical noteFunding Information:
Manuscript received March 3, 2000; revised August 29, 2000. This work was supported by Brain Korea 21 Project. H. J. Lee and J. B. Park are with the Department of Electrical and Computer Engineering, Yonsei University 120-749, Seoul, Korea. G. Chen is with the Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204 USA, and also with the Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong. Publisher Item Identifier S 1063-6706(01)01357-1.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computational Theory and Mathematics
- Artificial Intelligence
- Applied Mathematics