Analysis and design of multivariable extremum seeking

The paper provides a multivariable extremum seeking scheme, the first for systems with general time-varying parameters. We derive a stability test in a simple SISO format and develop a systematic design algorithm based on standard LTI control techniques to satisfy the stability test. We also supply an analytical quantification of the level of design difficulty in terms of the number of parameters and in terms of the shape of the unknown equilibrium map. Moreover, we remove the requirement of slow forcing for plants with strictly proper output dynamics (and consequent slow convergence) present in earlier works.