Source localization problem with autonomous agents in the form of single-agent or multi-agent is one of the active research fields in control. Source localization with the autonomous agents commonly has been done by processing of data that is obtained from localization equipments. Because of inacessebility to the localization equipments' data in circumstances such as under water, ice and furthermore the big-budget of inertial navigation systems, source localization problem without using of localization equipment had been one of the considerable cases in the recent decades. In the source localization problem without localization equipments, it is assumed that the agent is in a signal's field neighbor and that is used for seeking signal's source. The distribution of the signal's field is unknown, however the intensity of the signal decreases as gets away from the source.The only available data to control the agent is the data that has been received from the online-measuring of the signal's field by a sensor, which is located on the autonomous agent. Notes that the main purpose of agent is seeking a location corresponded to the maximum signal's value, extremum seeking control as an non-model based optimizatio is a suitable tool for source localization problem.In the recent years source localization with the first-order integrator, second-order integrator and non-holonomic agents has been studied. The non-holonomic agent is cotrolled by tuning of its forward and angular velocities. The unsuitable performance of the non-holonomic agents in the transient and steady states is because of applying permanent excitation signals in their localizatio schemes. Recently a new scheme for source localization by non-holonomic agent is proposed in which permanent excitation signals arenot applied in it that causes improving its performance in transient and steady states. In this scheme, one of the angular or forward velocities of the nonholonomic agent is being fixed at a constant value and the other one is controlled by suitable filtering of its output value. By assuming a quadratic distribution of a signal's field, exponential stability of this scheme is proved based on averaging theory. Angular and forward velocities of the agent in this scheme are being controlled without a specified bound. In this thesis, this scheme is being modified such that the angular velocity of the agent has a specified and tunable bound. by this means, its angular velocity control law being normalized suitably. Using the normalizer formation make stability analisi too complicated and impossible for applying averaging theory. Therefore, stability analisis of the modified scheme has been done by Lie brackets and singular perturbations theory. In this case, global uniform practical asymptotical stability (SPUAS) of the proposed source localization scheme in 2-D and 3-D with any kind of the distribution of a signal's field ( not necessarily quadratic ) is being proved by two theorems. Computer simulatio confirm the accuracy of theoretical results. Also, these simulations shows the robust performance of the normalized angular velocity control law against changes and uncertainties of the parameters of the signal's field distribution map. 1- Source localization, 2- Extremum seeking control, 3- Nonholonomic agent, 4- Practical Stability, 5- Bounded angular velocity