Extremum seeking control for discrete-time systems. (Technical Notes and Correspondence)

We present an extremum seeking control algorithm for discrete-time systems applied to a class of plants that are represented as a series combination of a linear input dynamics, a static nonlinearity with an extremum, and a linear output dynamics. By using the two-time scale averaging theory, we derive a mild sufficient condition under which the plant output exponentially converges to an [OMICRON] ([[alpha].sup.2]) neighborhood of the extremum value, where [alpha] is the magnitude of modulation signal. The sufficient condition is related to positive realness of linear parts of the plant but only at the modulation frequency. The algorithm is illustrated with a brief simulation study. Index Terms--Averaging, discrete-time systems, extremum seeking.