Abstract
This paper offers a wide research survey on analytical strategies for characterizing large asymptotic stability domain identified with Lyapunov's methodology. It depicts an advanced based Particle Swarm Optimization (PSO) technique which performs swift and precise investigation, and characterizes high-performance and exact attraction domains for the class of nonlinear affine systems. The synthesized step algorithm is implemented to analyze the stability problem depending on indirect Lyapunov's theory. Illustrative benchmark models and numerical simulation analysis are provided to validate the effectiveness and the efficiency of the proposed procedure.