This paper presents a methodology for the synthesis of a self-organizing control system for a single-input single-output object within the class of two-parameter structurally stable mappings. The proposed approach is based on a Lyapunov framework using a gradient-type method applied to Lyapunov vector functions. Conditions defining aperiodic robust stability of stationary states are derived for both the control system and its corresponding model with prescribed transient characteristics. These conditions are formulated as parameter inequalities that define admissible regions ensuring non-oscillatory convergence of system trajectories. The obtained stability conditions are used to compute the controller coefficients, establishing a relationship between system parameters and admissible stability regions. Simulation results show that the state trajectories converge to the equilibrium point, while the control signal remains bounded. The transient response is well damped and does not exhibit oscillatory behavior. The results demonstrate that the proposed approach can be applied to the design of control systems operating under parametric uncertainty.