Abstract
Till now, there are lots of stability and stabilization results about T-S (Takagi-Sugeno) fuzzy systems with time delay, but most of them are independent of the analysis of membership functions. Since the membership functions are an essential component to make a fuzzy system different from others, the conditions without its information are conservative. In this brief paper, a new Lyapunov-Krasovskii functional is designed to investigate the stability and stabilization of continuous-time T-S fuzzy systems with time delay. Different from the existing results in the literature, the integrand of the Lyapunov-Krasovskii functional in this paper depends not only on the integral variable but also on the membership functions, and thus, the information of the time-derivative of membership functions can also be used to reduce the conservativeness of finding the maximum delay bounds. Utilizing the information of the time-derivative of membership, a bunch of controllers are designed according to their sign, and then a switching idea is applied to stabilize the fuzzy system. In the end, two examples are given to illustrate the feasibility and validity of the design and analysis.
| Original language | English |
|---|---|
| Number of pages | 6 |
| Journal | IEEE Transactions on Fuzzy Systems |
| Issue number | 99 |
| Early online date | 14 Sept 2017 |
| DOIs | |
| Publication status | E-pub ahead of print - 14 Sept 2017 |
Keywords
- Membership dependent Lyapunov-Krasovskii function
- Parallel distributed compensation law
- Takagi-Sugenos fuzzy model
- Time delay