Dynamic Fuzzy Machine Learning

Theorem 1.10 If the disturbance system (1.30) is quadratic stable, the closed-loop dynamic fuzzy control system (1.26) is asymptotically stable.

Proof: The perturbed system (1.30) is quadratic stable according to definition (1.10):

For the closed-loop dynamic fuzzy control system (1.26), we have the Lyapunov function

where $\left(\stackrel{\leftharpoonup }{P},\stackrel{\rightharpoonup }{P}\right)$ is a dynamic fuzzy symmetric positive definite matrix. As the system global representation matrix $\left(\stackrel{\leftharpoonup }{C},\stackrel{\rightharpoonup }{C}\right)$ is an interval matrix, and $\left(\stackrel{\leftharpoonup }{C},\stackrel{\rightharpoonup }{C}\right)=(\left({\stackrel{\leftharpoonup }{C}}_0,{\stackrel{\rightharpoonup }{C}}_0\right)+$$($