IOTA-1-OPTIMALITY OF FEEDBACK-CONTROL SYSTEMS - THE SISO DISCRETE-TIME CASE

In this note, we study the problem of determining when a stabilizing controller is l1-optimal for a given plant for some stable weighting function. This problem belongs to the class of inverse problems in optimal control introduced by Kalman in 1964. We show that for a given plant, the set of all the H∞ -optimal controllers, obtained by considering all stable weighting functions with no zeros on the unit circle, is actually contained in the corresponding set of l1-optimal controllers. We also show that an l1-optimal controller (unlike an H∞-optimal controller) can remain l1-optimal for the same plant for a wide range of nontrivially different weighting functions. © 1990 IEEE