Abstract: The article deals with the problem of control synthesis for nonlinear dynamical systems represented by mathematical models with a linear structure and state-dependent parameters (SDC-model). The value that the Hamiltonian takes for suboptimal control synthesized using the model for an unlimited control time interval is established. A new parametric control algorithm is developed that uses the behavior of the Hamiltonian under the appropriate and state of the system. In general, a condition is obtained under which this algorithm provides asymptotic stability of the original control system.