We remove the long standing restriction that plant dynamics in extremurn seeking control must be stable and provide an extension that allows single integrators, double integrators, and moderately unstable single poles. An application of the result for single and double integrators is in control of autonomous vehicles. Extremum seeking is used for finding a source of a signal (chemical, electromagnetic, etc.) whose strength decays with the distance. This is achieved without the measurement of the position vector and using only the measurement of the scalar signal. (c) 2007 Elsevier Ltd. All rights reserved.