System identification for H∞ control

Some preliminary results are presented on a new method of identification for discrete time linear systems. The method is required to operate on experimentally determined, noisy frequency response data and is specifically required to yield a model which facilitates the design of robust controllers in the infinity norm. The philosophy underlying this method is not only to provide a robust identification algorithm but more importantly to emphasize minimization of the error bound between the true plant and the model. It is the reduction of this bound that allows improved performance to be obtained by the closed loop system when controlled by an H^∞ controller. The bound of this new method is computable from the a priori information of the plant´s relative stability properties and the noise´s bound as well as the a posteriori information of the plant´s noisy frequency response. The plant transfer function must be in the class of stable, causal, time invariant linear systems. The best method obtained to data is presented, and it is shown that its theoretical error bounds are smaller than those of other methods in the literature. Theoretical examples are included to demonstrate the method´s performance