Dynamic Fuzzy Machine Learning

(1.8) can be rewritten as

Since the right side of (1.9) is equal to $\left(\overleftarrow{0},\overrightarrow{0}\right)\text{when}\left(\overleftarrow{X},\overrightarrow{X}\right)\left(k\right)=\left(\overleftarrow{0},\overrightarrow{0}\right),$ the origin $\left(\overleftarrow{0},\overrightarrow{0}\right)$ in the domain is the equilibrium point of (1.9).

Theorem 1.3 The equilibrium point $\left(\overleftarrow{0},\overrightarrow{0}\right)$ of (1.9) of the DFMLS is globally asymptotically stable. If there exists a positive dynamic fuzzy matrix $\left(\overleftarrow{P},\overrightarrow{P}\right),$ then [18]

Proof: Consider the following Lyapunov ...