Stabilization of Nonlinear Control Systems through Using Zobov’s Theorem and Neural Networks

Zobov’s Theorem is one of the theorems which indicate the conditions for the stability of a nonlinear system with specific attraction region. We have applied neural networks to approximate some functions mentioned in Zobov’s theorem in order to find the controller of a nonlinear controlled system whose law in a mathematical manner is difficult to make. Finally, the effectiveness and the applicability of the proposed method are demonstrated through using numerical examples.