Abstract
This paper is concerned with the problem of membership-function-dependent controller design for a class of discrete-time T-S fuzzy systems. Based on the partition method of premise variable space, the original T-S fuzzy model is equivalently converted into a kind of piecewise-fuzzy system. Then by employing some staircase functions, the continuous membership functions are approximated by a series of discrete values, via which the information of membership functions is brought into the stability analysis to reduce the design conservatism. With piecewise Lyapunov functions, the approaches to the piecewise-fuzzy state feedback and observer-based output feedback controller design are proposed, respectively, in terms of linear matrix inequalities such that the closed-loop system is asymptotically stable with a prescribed <formula><tex>$\mathcal{H}_{\infty}$</tex></formula> performance level. It is shown that the membership functions of the fuzzy model and fuzzy controllers are not necessarily the same, which allows more design flexibility. Finally, two illustrative examples are provided to show the effectiveness of the developed methods.
| Original language | English |
|---|---|
| Journal | IEEE Transactions on Fuzzy Systems |
| Early online date | 9 Nov 2018 |
| DOIs | |
| Publication status | E-pub ahead of print - 9 Nov 2018 |
Keywords
- Analytical models
- controller design
- Fuzzy systems
- imperfect premise matching
- Linear matrix inequalities
- Lyapounv stability
- Lyapunov methods
- membershipfunction-dependent
- Stability analysis
- State feedback
- Symmetric matrices
- Takagi-Sugeno fuzzy systems