This paper investigates the state-space mapping-based framework to identify deterministic nonlinear systems. The main intent is to introduce an innovative identification inroad by using nonlinear error mappings and to explore the theoretical aspects of the application of Lyapunov＇s stability theory to systematically explore the convergence. This approach offers innovative and promising results. The Lyapunov stability theory has been widely used in stability analysis, and this paper demonstrates the application of the second method from parameter convergence perspectives. The systematic identification concept is introduced, and a novel scheme is developed by applying nonlinear error mappings. Another contribution is to demonstrate that in order to analyze the convergence, the nonquadratic Lyapunov candidates can be used. The unknown parameters of an electric drive, actuated by a permanent-magnet synchronous motor, are identified by using the experimental data. The example supports the procedure, and the simulation shows that the model dynamics match the experimentally measured states.