l/sub 1/-optimality of feedback control systems: the SISO discrete-time case

Controllers that optimally reject a class of disturbances are considered. The problem of determining when a stabilizing control is l/sub 1/-optimal for a given plant is studied for some stable weighting function. This problem belongs to the class of inverse problems in optimal control introduced by Kalman. It is shown that for a given plant, the set of all the H/sub infinity /-optimal controllers (obtained by considering all stable weighting functions with no zeros on the unit circle) is actually contained in the corresponding set of l/sub 1/-optimal controllers. It is also demonstrated that an l/sub 1/-optimal controller, unlike an H/sub infinity /-optimal controller, can remain l/sub 1/-optimal for the same plant for a wide range of nontrivially different weighting functions.<
>