Methods and systems for impedance matching between loads and power generators are provided. The methods include: supplying a power generated by a power generator to a load by an impedance matching system that includes at least one reactance adjustable by at least one actuator and is configured to transform the load impedance at an input end of the load into a transformed load impedance at an input end of the impedance matching system, determining a power reflected at the load or at least one variable associated with the reflected power, determining, based on the reflected power or the at least one variable, that there is a mismatch, determining a trajectory in a complex load plane according to at least one specified criterion, and controlling the at least one actuator such that the transformed load impedance follows the trajectory to match an output impedance of the power generator.