The design of asymptotic stabilising controllers for slowly varying nonlinear systems is considered in this paper. The designed control law is based on finding a slowly varying control Lyapunov function. Also, consideration of the Hamilton-Jacobi-Bellman equation showed that the proposed controller is a suboptimal controller and the response of the system may be very close to its optimal solution. The maximum admissible rate of changes of the system dynamic is also evaluated. This technique is first applied to a created example and then to a practical example (optimal autopilot design for an air vehicle). The air vehicle is modelled as a nonlinear slowly varying system and the efficiency of the designed autopilot in terms of transient responses, control signals and the values of cost function are shown by numerical simulations.