araujorayza/cnmac2023

This repo contains the code for implementing example 3.1 of paper Invariance Principle and the Asymptotic Behavior of T-S Fuzzy Systems.

CNMAC2023

This repo contains the code for implementing example 3.1 of paper Invariance Principle and the Asymptotic Behavior of T-S Fuzzy Systems.

Contents

This repo contains

README.md	This file
example3_1.m	Example 3.1 script
CNMAC_2023_Fuzzy.pdf	Preprint .pdf version of the paper
LICENSE	GNU General Public License v3.0

Requirements

• Matlab R2021b
• Sedumi
• Yalmip

How to use it

Open the example3_1.m file in matlab and run the script. The three figures below should open.

Figure 1 shows the graph of $V(x)$ inside set $Z$. The minimum value of $V$ in the boundary of $Z$ is $b$.

Figure 2 shows the contour plot of $V$ superposed by the boundary of set $\mathcal{D}$, in black. Using the level sets, we can find $l$, the maximum value of $V$ inside $\mathcal{D}$.

Figure 3 shows the level sets $\Omega_L,\Omega_l$ and the set $\mathcal{D}$.

Citation

If you find this paper useful, please cite it in your publication using the following bibtex entry:

@inproceedings{araujoInvariancePrincipleAsymptotic2023,
  title = {Invariance Principle and the Asymptotic Behavior of T-S Fuzzy Systems},
  booktitle = {Proceeding Series of the Brazilian Society of Computational and Applied Mathematics},
  author = {Araujo, Rayza and Alberto, Luis Fernando Costa and Valentino, Michele Cristina},
  year = {2023},
  address = {{Bonito, MS, Brazil.}}
}