Abstract
This chapter presents the stability analysis and performance design for nonlinear systems. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the nonlinear plant. A fuzzy controller with enhanced stabilization ability is proposed to close the feedback loop. Membership functions different from those of the fuzzy model are used by the fuzzy controller to simplify its structure. However, under such a case, an imperfect premise-matching condition is resulted, which will lead to conservative stability conditions. To reduce the conservativeness, the information of the membership functions of the fuzzy model and controller is employed. The enhanced stabilization ability of the fuzzy controller is able to further relax the stability conditions. However, the stability conditions derived using the Lyaunov-based approach are in the form of bilinear matrix inequalities (BMIs) of which the solution is difficult to be found. The genetic-algorithm based convex programming technique is proposed to solve the solution of the BMIs. BMI-performance conditions subject to a scalar performance index are derived to guarantee the system performance. Simulation examples are given to illustrate that the proposed approach can provide a systematic and effective way to help design stable and well-performed fuzzy-model-based control systems.
| Original language | English |
|---|---|
| Title of host publication | Foundations of Generic Optimization: Volume 2: Applications of Fuzzy Control, Genetic Algorithms and Neural Networks |
| Editors | R Lowen, A. Verschoren |
| Publisher | Springer |
| Pages | 261 - 281 |
| Number of pages | 21 |
| Publication status | Published - 2007 |